"Black holes are macroscopic objects with masses varying from a few solar masses to millions of solar masses. To the extent they may be considered as stationary and isolated, to that extent, they are all, every single one of them, described exactly by the Kerr solution. This is the only instance we have of an exact description of a macroscopic object. Macroscopic objects, as we see them all around us, are governed by a variety of forces, derived from a variety of approximations to a variety of physical theories. In contrast, the only elements in the construction of black holes are our basic concepts of space and time. They are, thus, almost by definition, the most perfect macroscopic objects there are in the universe. And since the general theory of relativity provides a single unique twoparameter family of solutions for their description, they are the simplest objects as well."
 S. Chandrasekhar ( IndianAmerican astrophysicist, 1910  1995, Punjab, British India; "The Mathematical Theory of Black Holes", first published 1983, 1992, 2000, 2009, Oxford University Press )
"As the atom is the basic unit for matter, so the orbit is the basic unit for understanding the universe"  Michio Kaku
"A black hole is a waterfall of space where space itself is falling faster than light"  author unknown
source: Quanta Magazine with David Kaplan
The Geometry of Spaces: A Thumbnail History
The geometry of space, in most simplest terms, begins with Euclid ( mid4th  mid3rd century BC; born where? residence Alexandria, Hellenistic Egypt; mathematician, philosopher; author "Elements" ) and Pythagorus ( born c.569 BC  died c. 475  495 BC; of Samos, Ionia; Greek mathematician and philosopher )'s right triangle hypotenuse theorem, say, without any idea or mention of time. Much later in the analytic geometry of René Descartes ( 1596  1650, Kingdom of France, mathematician and philosopher ), his methods of applying algebra to spaces is today widely, no universally, accepted where describes a 3dimensional space in socalled Cartesian coordinates or axes. Still nothing about time or even a hint of an idea of time.
About the same time of Descartes, Isaac Newton ( 1643  1727, England ) and Gottfried Leibniz ( 1646  1716, Holy Roman Empire, Germany ) introduced absolute time into their differential calculus equations of motion. But, still, the geometry of spaces was essentially maintained without any significant or deep thought given as to what exactly is 'time'.
Now, of course, the author of Relativity Physics and Science Calculator has come to define time as an accounting for the relative motion of objects: no objects, no time; and no motion, no time. Furthermore, by the philosophic "law of indiscernibles" you cannot distinguish actual time from a given clock which measures such time. That is, in the ontological identity of indiscernibles, you cannot separate one entity from the other, namely time from the clock which measures it and vice versa. They are one and the same in the broadest sense of meaning for both clock and time! Get used to it! EarthSun. A big clock in the sky, for example. In the Bible somewhere ( Joshua 10: 1213 ), Earth stands still: or haschehmesh vayyiddōm. That is, in relation to the Sun. If so, then time stopped. In fact, time did not even exist! No need for such time, truth be told.
Getting back to describing spaces, Einstein's genius was in introducing the idea of time into the geometry of spaces. For example, when you want to meet someone at such and such a location, you use a common sense sort of analytic geometry devised by René Descartes in setting forth a location in longitude and latitude measures. And you also assign a time to such a meeting. No? Yes. So now you have 4 elements or coordinates in the barest manner describing where and when the meeting will take place. Such is the nature of abstract reasoning. No emotions, just analytic mathematical thinking so to speak. We humans do this all the time, no pun intended.
Ok, so we've now incorporated a 4thdimension or coordinate axis into our analytic geometry of spaces and in terms of this newer pseudoEuclidean geometry we utilize a straight arrow ( actually not so "straight" when gravity is involved! ) of light photons to outline our axes. But time is still sort of in our imagination superimposed onto the 3d Cartesian dimensions of , and axes. In fact, time is assigned to a socalled "imaginary axis" of which itself comports with the square root of (1), an imaginary number if ever there be such. Again, yes!
Continuing, so ok, we have our and now coordinate axes describing a volume of space in analytic or pseudoEuclidean geometry which we term .
Question: how come or mass is somehow inserted into this newest sort of geometry? Simple. Einstein insisted that time, that 4th axis of geometry, is affected by gravity, fields of gravity in fact. So with what do we associate gravity? Mass, of course, Silly We! More mass , more gravity, and hence somehow time itself is affected. How so? Remember by the philosophic "law ( or identity ) of indiscernibles", time and the clock which measures it are one and the same thing. And with a field of gravity introduced into our analytic geometry of spaces by bringing mass into the understanding of physical spaces, our spaceandtime metric or yardstick must therefore also incorporate a mass . Yes! Oh, I forgot to mention, most critically, that gravity  indiscernible from mass  affects a clock by slowing it down and hence, by logic, gravity slows down time! Yes, again!
What therefore follows in the history of science in every subsequent equation setting forth a geometry of spaces, gravity by way of a body of mass must be included. And it is. Thank you Jewish genius Albert Einstein!
One last thing to confuse but it’s really common sense: when we turn a corner in our car, going at a certain speed, we feel a bit of acceleration from changing direction in the way that our bodies are slightly twisted to one side or another. Einstein said that by such acceleration we actually are creating a bit of a ‘microgravity‘ field. Yes! And the clock attached to our wrist is thereby so ever slightly slowed down. Yes, again! Confused? You shouldn’t be once you think about the microgravity, or forces, an astronaut suffers in the rocket going to the International Space Station escaping the bonds of Earth’s gravity.
But Why Study Black Holes?
Roy Kerr: General Relativity and Black Holes
It is truly believed that in the deepest recesses of a black hole beyond the event horizon, there will be found a unifying mathematics for the science of the macrouniverse combined with the microrealm of quantum subatomic waveparticles which in turn could unleash untold amounts of secrets for eventual unlimited energy production for humanity's wellbeing.
Between Einstein's 1915  1916 discovery of the spacetime mathematics of General Relativity and Roy P. Kerr's 1963 discovery of the geometry of black hole rotation as a solution to Einstein's equations was some 27 years where any black hole spin affects spacetime in its immediate vicinity which in turn affects any matter in the surrounding accretion disk of dust and rock. Of course, any light emanating from the swirling accretion disk is used to account for the central black hole mass itself as well as its chemistry in the spectral analysis of such light. Further into the study of rotating black holes, especially coalescing pairs of rotating black holes, is the significant matter of gravitational wave production which was just confirmed in September, 2015 in audio form by the LIGO Experiment. Such probing of converging pairs of black holes by LIGO and soon enough more by Virgo, AURIGA, and MiniGRAIL, will give even deeper understanding of a universe which we inhabit.
A Few Short Definitions
Singularity: The gravitational field of the black hole body becomes so infinite that the laws of normal spacetime do not apply; denoted as .
Event horizon: The event horizon in the vicinity of an extremely compressed mass from which nothing can achieve "escape velocity" at the acknowledged upper limit for both kinetic energy and gravitational potential. That is, the Schwarzschild or gravitational radius is the radius of a compressed sphere containing all of the mass of a given object where the escape velocity from it is the speed of light.
Schwarzschild radius: The Schwarzschild ( gravitational ) radius is the black hole distance between the event horizon and its singularity.
Null geodesic: the worldlines of photons
Radial null geodesic: The worldlines of photons are moving directly towards or directly away from the singularity of the black hole.
Timelike: that part of spacetime where the normal causal laws of physics apply.
Lightlike: that existential "edge part" of a lightcone in spacetime where travels light photons; neither spacelike nor timelike as it separates one from the other.
Spacetime ( or spacetime, spacetime continuum ): a term of art describing a multitude of differing mathematical physics models combining the 3 dimensions of normal human perceptions with the imagined "dimension" or coordinate axis of time:
A Quick Course in the Topology of Black Hole Spacetime
As the geometry of shapes of spaces under conditions of continuous deforming stresses ( but not tearing or gluing ) becomes more difficult to quantitatively describe, if not impossible, the modern mathematics of topology however allows for making qualitative predictions for these same deformed shapes and spaces.
Topology as a major branch of modern mathematics [ ref.: "Analysis Situs" ('picking apart of place') first envisioned by Gottfried Leibniz ( 1646  1716, German, contemporary of Isaac Newton and cooriginator of the modern calculus ); Henri Poincaré ( 1854  1912, French ), published 1894 ] therefore grew out of "common geometry" utilizing "set theory" [ ref.: George Cantor ( 1845  1918, German, of speculative distantly removed Jewish ancestry by inherited genetics ), primary originator of the basic concepts of set theory including propounding the idea of an 'infinity of infinities' within the realm of the philosophy of mathematics.
§ Topological set theory definitions:
(i). a differentiable spacetime manifold with an associated of gravitational potentials written as a family atlas of pairs ;
(ii). spacetime is either causally "timelike" definable over a smooth nonvanishing vector field or "lightlike" ( equivalently a 'null geodesic' ) such as a stream of light photons; therefore not "spacelike" which otherwise resides in the realm of noncausal "Elsewhere";
(iii). the topology of the spacetime manifold residing in the number set of 3Euclidean real spacepoints plus 1 for time along an imaginary axis whose set of spacetime points is denoted as and translated as ;
(iv). the "lightlike" geometric topology boundary of spacetime as discerned by an infinitely distant observer is defined as all null geodesics ( light rays traversing along the 45^{o} edge(s) of a multitudinously infinite amount of lightcones  see: "The Null Geodesic" ) consisting of two disconnected spacetime "lightlike" regions beginning and ending such that "lightlike" region , satisfying Einstein's vacuum gravity equations where the energymomentum [ vector ] tensor decreases exponentially fast at infinity for which each "lightlike" region possesses topology
,
defines the totality of spacetime.
(v). the causal set of past "timeorientable" spacetime points definable over a smooth nonvanishing vector field is given as:
(vi). the causal set of future "timeorientable" spacetime points definable over a smooth nonvanishing vector field is hence given as:
However an allowance must still be made available in our speculative thinking for the hidden region of "spacelike" space of noncausal "Elsewhere" where causally propagated light signals have not yet reached the future space of light photons for human eyes to actually observe sometime in the future. That is, the "spacelike" space of noncausal "Elsewhere" is totally outside the bounds of any future spacetime possibility, by definition, unless by some quirk of an unknown gravitational force field such noncausal "Elsewhere" spacetime points are moved into a future causal realm of spacetimefuture .
§ Some conclusions:
a. the entire asymptotically flat ( defined by Penrose: 1963, 1964, 1965 & 1968 ) Minkowskian spacetime is defined by
b.
and will be causally disconnected from the rest of spacetime.
c.
image source: NASA
Black Hole Uniqueness
For this derivation see down below: 'The Horizon Function defines the Ergosphere'.
Proper Time vs. Coordinate Time
is 'proper time' which is literally time attached to the person's wrist for example. is 'coordinate time' which is the distant clock time viewed by a stationary observer(s) from a radial distance away.
For example, say there are two identical clocks sidebyside and both set simultaneous to the same exact time. One clock will stay with the stationary observer(s) on his/her wrist. This clock by definition gives 'proper time' which is always constant except of course for the normal time progression of this clock. But the second clock for 'coordinate time' will be moved away from the stationary observer(s) to some considerable distance with some significant velocity relative to the speed of light, the universally constant yardstick for measuring both distance and time.
Now even though both clocks had initially been simultaneously set to the same exact reading of time, only the proper time clock will remain constant in its time progression whether mechanical or atomic; however, the coordinate time clock will be viewed as having different time progressions by different stationary observers depending upon its distance and flyaway speed relative to each of the several stationary observers. Remember that these two clocks originally were set simultaneous to the same exact reading of time but now these couple of clocks will read different times!
Why? The real question is why the flyaway, coordinate clock differs from the stationary proper clock.
The answer comes in two parts: 1). special relativity and general relativity. More specifically, the universal constant speed of light of special ( and general! ) relativity, and gravity's acceleration of general relativity. In the case of special relativity, this reduces down to the doppler effect of light coming into the view of the distant, but stationary, observer. 2). In the case of general relativity, the effects of gravity arising from the accelerations affecting the coordinate clock as it flies away at a considerable magnitude relativity to the speed of light. Explaining a bit more in detail, the further away is the coordinate clock, the slower by doppler effect will time progress to the distant yet stationary observer(s). And the faster the coordinate clock flies away, the slower yet will the coordinate clock appear to the stationary observer(s). Assuming, of course, that there's a powerful enough telescope to peer directly into the distant time movements of the coordinate clock's mechanical hands or atomic radioactive emanations.
So, the point is, proper time and coordinate time will differ by a certain amount based upon the mathematics of Einstein's relativity physics. But not all is lost since the same mathematics of relativity relates coordinate time to proper time. That is, knowing coordinate or proper clock times, either can be derived from the other using the same mathematics of relativity. Hence, problem solved!
Spacetime Metrics
Kerr's Unifying Equation: Revealing Other Metrics
A Standard Clock at Rest at Spacial Infinity
Conclusion: since no particle or physical object can reside in a spacelike ( "Elsewhere" ) interval realm for otherwise it would have to move faster than , the speed of light, therefore any body or particle possessing mass cannot remain stationary inside the Schwarzschild gravitational radius of and will consequently move inwards towards the central singularity of in much the same analogous way that time's arrow always moves forward, never backwards. In the opposite case of a White hole, the body of mass will move away from the central singularity.
The Event Horizon: The Schwarzschild Escape Velocity
See: "Black Holes Event Horizon and Escape Velocity" at http://www.relativitycalculator.com/appendix.shtml
Also: "The Schwarzschild Equation" at http://www.relativitycalculator.com/password_protected_files/schwarzschild_equation.shtml
The Geodesic Worldline Trajectory of Free Photon Radial Motion Crossing the Event Horizon passing immediately into the Black Hole Singularity
( that is, inescapably the future of every event inside the event horizon is inexorably "already" at the singularity )
The Minkowski Light Cone in Flat Spacetime
The Eddington  Finkelstein coordinate system maintains the Schwarzschild null light cone surfaces along 45^{°} slants just as they would be in flat Minkowski spacetime for the overall mathematical sake of consistency in black hole physics.
The Eddington  Finkelstein Coordinates
The Eddington  Finkelstein "hybrid" coordinates ( discovered Eddington 1924; rediscovered Finkelstein 1958 ) and replace the Schwarzschild coordinates which otherwise become singular ( i.e., undefined ) at the event horizon, or simply , where the time interval becomes expansively infinite ( clock time "stops" ) but yet the infalling radial photons continue past the event horizon without any outside observer acknowledgement. And in this sense information as to infalling photons becomes "lost" thus contradicting the principle of conservation of information whereas any such physical probe sent thru the event horizon will continue unhindered if not entirely squished by the black hole's gravity.
Therefore the Schwarzschild time coordinate of radially moving photons towards and into a black hole
is replaced by the "Regge  Wheeler tortoise coordinate" in order to fully account for the trajectory of any such physical probe sent thru the event horizon:
which must satisfy:
See above: Now notice how earlier suggestive relationships dovetail into later equations:
Eddington  Finkelstein defines new "proper time" light cone null coordinates = constantly drawn sloping 45^{0} lines ( see above: 'The Minkowski Light Cone in Flat Spacetime' ), rather than as surface planes where is a physical singularity as opposed to a coordinate singularity at , the latter of which can be transformed away by another coordinate transformation, such as follows:
That is, the Eddington  Finkelstein tortoise coordinates are intended to smoothly and continuously go to infinity as any undefined and unwanted singularity is approached. And the unmitigated importance of tortoise as it ranges from  infinity to + infinity becomes obvious to any outside objective observers as the entire Schwarzschild spacetime is observable and hence accessible without any intervening singularities!
Furthermore and most importantly, the Eddington  Finkelstein coordinate system converts the Schwarzschild metric into a null geodesic 3surface ( the gravity potential becomes infinite at the event horizon boundary ) of infinite redshift ( all time clocks stop at the event horizon boundary ), having a lightlike line element lying along the Schwarzschild event horizon surface , while maintaining in this spherically symmetric Schwarzschild geometry of Eddington  Finkelstein coordinates all lightcones possess ± 45^{0} sloping sides. And as the distance from the black hole singularity , the symmetrically spherical Schwarzschild spacetime geometry devolves to the asymptotically flat Minkowski spacetime geometry devoid of any mass and hence gravity.
♦ Lastly, for all that has been insightful so far in utilizing Eddington  Finkelstein, so also by incorporating the Eddington  Finkelstein coordinates into the Schwarzschild geometry metric we effectively gain some greater amounts of the mathematics for white holes and wormholes in addition to black holes!
The Schwarzschild Spacetime Metric for Black ( White ) Holes in Eddington  Finkelstein Canonical Coordinates
Again, but this time for the full 3dimensional Schwarzschild spherical metric using the Eddington  Finkelstein canonical coordinates:
The Horizon Function defines the Ergosphere  Part 1
Black Hole Inertial Frame Dragging
( Black Hole Angular Velocity / Momentum )
source: David Butler  YouTube
By Yukterez (Simon Tyran, Vienna)
spacetime geometry precession in the black hole rotational twisting
The Binary Mass Function
( or, how massive is any given black hole )
§ Solution to the 2body problem for black holes:
§ Derivation of the binary mass function:
Distance: Redshift, Hubble's Constant and Black holes
§ Brand new method ( 02/2013 ) for measuring cosmic distances using accreting Black Holes:
Using well established cosmology techniques for measuring black hole masses by the amount of accreting falling masses, a black hole's energy at the event horizon can be fairly well measured according to a recent paper by Prof. Hagai Netzer of Tel Aviv University, Israel, along with Jian  Min Wang, Pu Du and Chen Hu of the Institute of High Energy Physics of the Chinese Academy of Sciences and Dr. David Valls  Gabaud of the Observatoire de Paris. This energy can then be compared to the amount of energy radiation from a given black hole reaching earth in determining the universe's rate of expansion and hence very large cosmic distances with a very high degree of accuracy. See: "Super  Eddington Accreting Massive Black Holes as Long  Lived Cosmological Standards", publication date: 02/2013, reference: 2013PhRvL.110h1301W, Physical Review Letters, vol. 110, Issue 8, id. 081301.
published: Nature 458, 820824 (2009)  doi:10.1038/458820a / source: NASA/WMAP SCIENCE TEAM
Hubble's constant is rather indeterminant at this stage of understanding in cosmology science but, nevertheless, Hubble's Law suggests not without reason that the circumference of the entire universe ( matter, dark matter, dark energy, spacetime itself ) is expanding outward at an accelerating rate.
The ≈ 71 kilometers per second per megaparsec ( about 3.3 million lightyears ) means that for every 3.3 million lightyears a galaxy ( or black hole ) is further away from us, the galaxy ( or black hole ) is moving another ≈ 71 kilometers per second faster away from us.
§ Another method for measuring cosmic distances using accreting Black Holes, Energy Redshift and Hubble's Constant:
Remember,
The Black Hole as a Hologram
( or, how the hologram paradigm rescues information )
Information, Entropy and Energy are three Inseparable Qualities of Black Holes
§ What do we actually know about a black hole as an observer on the outside?
image source: http://www.scholarpedia.org/article/BekensteinHawking_entropy
That is, the only exterior information available to a distant observer of a black hole are its mass M, angular momentum J, and its electric charge Q due to the electromagnet limitations imposed by the interior light cone.
§ The Problem of Information Loss  aka the Information Paradox:
Throughout all of mathematical physics, there is a basic premise that neither energy nor its equivalent mass can be either created or destroyed. It's called the 'Conservation of Mass  Energy'. However, in simplest terms, this basic assumption breaks down when considering black holes and its event horizon beyond which nothing can ever be retrieved for some sort of reconstitution outside the black hole. And this especially concerns the socalled "information" of the different quantum states for electrons, protons, muons, quarks, etc. at the microsubatomic level which nevertheless still constitutes the substrata of the overriding macroworld in which we indeed live after all. In other words, if somehow theoretically mathematical physics could retrieve "information" from the deep, dark depths of black holes and their surface event horizons, then the physics of black holes could be brought back into the realm of larger physics, so to speak, and hence 'Conservation of Information' is thereby maintained.
♦ note: the á priori conservation premise of massenergy is accepted as a "science faith" proposition which cannot be proven as immutably true from now until the indefinite future but is simply operationally accepted as workable. Shocking!
§ A solution to the Information Loss paradox  a brief outline sketch:
massenergyinformation is conserved  i.e., nothing is lost but individual molecule information is hidden;
theoretically individual molecular information of particular molecules, atoms can still be retrieved
4 laws of black hole mechanics vs. 4 Laws of thermodynamics these laws are respectively analogous to each other 


black holes  thermodynamics  
zeroth law  uniform event horizon surface gravity g_{rr}  ⟺  uniform T throughout closed system  
1st law  dM ∝ dA
(conservation of mass) 
⟺  dE = T dS (conservation of energy) 

2nd law  event horizon area only increases, never decreases  ⟺  entropy only increases, never decreases  
3rd law  g_{rr} ≠ 0, g_{rr} > 0; in fact, g_{rr} → ∞
(impossibility zero surface gravity) 
⟺  T ≠ 0, T > 0
(impossible absolute zero temperature) 
black hole physics vs. laws of thermodynamics where these corresponding entities are respectively derived from each other 


black holes  thermodynamics  
mass M  ⟺  energy E  
event horizon surface gravity g_{rr}^{∗}  ⟺  temperature T  
event horizon area A^{∗∗} ( entropy is related to area, not volume! ) 
⟺  entropy S  

Stephen Hawkings proved in the proximate vicinity of the event horizon, virtual particles from the quantum vacuum fluctuations
of the gravitational field are converted into real pairs ( particles / antiparticles ) where energy conservation is preserved.
In Stephen Hawking's black hole research, he derived the idea that in the proximate gravity of the event horizon, otherwise virtual particles become real on a macro timescale where energy conservation is maintained permanently due to the extremely short time intervals involved. Normally, however, energy conservation would be violated for such virtual particle and antiparticle pairs on much longer time intervals but energy conservation is nevertheless maintained as virtual particles instantaneously annihilate their antiparticle counterparts.
Therefore to some distant observer at infinity, the black hole radiates a real particle with positive energy which will be offset by a corresponding real antiparticle with negative energy entering; hence, black holes radiate positive energies like other blackbodies while losing mass thru evaporation by absorbing real negative antiparticles!
Thus energy is conserved and furthermore, as will be theorized ( see: 'Holographic Principle' down below ), quantum information of subatomic particles itself is preserved across the entirety of the 2 ( or 3 ) dimensional surface of the event horizon.
Stephen Hawking quote: "The information will be reemitted when the black hole evaporates", NYTimes, Oct. 23, 2018, by Dennis Overbye.
The BekensteinHawking black hole entropy is defined for 1/4th of the entire black hole horizon area per one (1) Planck area unit
Then to Hawking's great intellect, he associated a field system containing a distribution of particles with a thermal (heat) number distribution in the proximate vacinity of the event horizon of a Schwarzschild black hole as viewed by a far distant observer at infinity in a vacuum of lowest energy state for flat Minkowski spacetime:
What is amazing of the BekensteinHawking entropy equation is that as the information of "stuff" gets sucked into a black hole, the volume per se does not increase but rather the surface horizon area does! And the maximum limit of the amount of information that a black hole can contain is determined by the entropy of the black hole where the maximum entropy in a region of space is one bit per Planck area.
Further proof of this relation between horizon area ( hence entropy ) and matter falling into a black hole, can be clearly shown as:
for which
where adding matter incrementally
The holographic principle in simplest words stipulates that information for matter ( subatomic particles comprised of mass, location, spin, quantum flavors of "color", "top", "bottom", angular momentum, electric charge, etc. ) that has fallen into a black hole can be retrieved from the lowerdimensional ( 2 or 3 dimensions ) event horizon to arrive at the higher 3 dimensions or Einstein's 4 dimensions with which we have become familiar. Saying this again, all the supposed "disappeared" particle information flying into the black hole can be retrieved or read, so to speak, from the quantum 'string physics' smearing ( Yiddish slang: 'schmearing' ) of antiparticles onto the surface of the holographic event horizon of the black hole just like we see 3dimensions derived from a 2dimensional flat surface such as on your credit card.
This mathematical physics insight has profound philosophic implications for the world, hence universe, in which we live.
§ Einstein's 'Spooky action at a distance':
Before delving further into any philosophic implications from what has already proceeded, it would be remiss to neglect to ponder Einstein's 'Spooky action at a distance' which may indeed intimately connect up with the holographic principle in the sense that what comes into our eyes as a 3 or 4dimensional projected hologram reality from the furtherest extent of the event horizon of the universe itself is 'spooky action from a far distant' existence of quantum reality!!
Read:
"Spooky Action", by Ronald Hanson and Krister Shalm, Scientific American  Volume 319, Issue 6, December, 2018.
"Bell inequality explaining quantum correlations: Spooky Action at a distance  slides", by Robin Harper, University of Sydney.
"Experimental loopholefree violation of a Bell inequality using entangled electron spins separated by 1.3 km", by Ronald Hanson, et al., Delft University of Technology, Delft, The Netherlands; doi: 10.1038/nature15759, published 2015.
source: TU Delft  Delft University of Technology; hansonlab.tudelft.nl
Some Preliminary Philosophic Speculations
The author of Relativity Physics and Science Calculator is now inclined to try to further understand black holes as holograms which leads to a deeper possibility of, perhaps, our entire 3dimensional universe / cosmos as a projection of a 2dimensional, flat surface hologram!
That is, analogous to a black hole, we ourselves may be living inside some sort of immeasurable black hole and whereas we "see" 3dimensions of our world, it may be that we’re simply seeing a 2dimensional hologram schmeered across the event horizon of the Grandest, outermost black hole in which we’re immersed.
[ note: think back to Ernest Mach ( as in Mach or gforce )’s Conjecture Principle of Inertia and Centrifugal Force. See: http://www.relativitycalculator.com/mach_principle_inertia.shtml ]
Again: we look and see 3dimensions imprinted into our 2dimensional credit cards of the small encrypted square. So 3dimensions comes into our human eyes of the encoded square from a flat 2dimensional hologram imprinted into the credit card. That is, 2dimensional geometry of a space produces the "reality" of an illusory 3dimensional space. It’s a true illusion. Yes, it’s an hologram.
Ok, so what if when we’re seeing 3dimensions it actually is being produced as a projection to our human eyes by a 2dimensional event horizon of the furthest, outermost black hole in which we’re immersed? Could be.
Now why should this be true?
Well, black holes are true as has been shown recently [ September, 2015; published February, 2016 ] in producing Einstein's gravitational waves in the merging of two (2) swirling black holes.
See: http://www.relativitycalculator.com/gravitational_waves_definitively_detected.shtml
But we don’t actually know what goes on inside a black hole. Not in any naïve realism of our 5senses. In fact, truthfully, our 5senses tell us little of what’s going on around us. Television waves. Radio waves. Radiation waves. Cosmic wave rays. That we’re flying around the sun on a rock we call earth without feeling any motion. That germs exist to help or kill us. To a religious person: God exists, Heaven exists, the "spiritual dimension" of humans exists. To an atheistic physicist: 4dimensions and up to 11dimensions exist. And so forth and so on …
However the mathematical physics of black holes involves entropy, subatomic quantum particle physics, conservation of massenergy and especially conservation of "information". Yes, information! Information itself must be conserved like mass & energy and cannot be lost to the world outside of the black hole. But black holes suck everything into themselves, nothing gets out, hence "information" is not conserved. But "information" must be conserved in order to maintain the logical consistency of the mathematical physics of our known external world. Following this?
The solution to this puzzle, conundrum or contradiction is to imagine that from inside a black hole there’s a hologram trying to get out to reach, in effect, our human eyes for constructing an illusory 3dimensional world for our "reality". But that’s just one, singular black hole. Maybe, however, there are black holes inside of black holes inside of other black holes ( multiverses ) for which the furthest, most outermost of the grandest black hole of All Black Holes is producing an illusory 3dimensional world of reality emanating from its own 2dimensional event horizon!! A hologram? Could be!
Hence, the study of black holes and the associated mathematical physics is delving closer and closer into deep philosophic questions of the meaning of "reality" of some sort of an "external world".
Therefore: External World ( as we humans perceive it! ) <==> a hologram coming to us from the Grandest, outermost black hole of the entire cosmos? Really??
But yet the mathematical physics of black holes is tentatively pointing to this philosophically tenuous conclusion.
Stay tuned, stay tuned …
§ Philosophic implications:
The review previously presented already of Hubble's Law is to emphasize that distances to the far reaches of black holes in the universe are also indeed subject to this same law of the cosmos. But what the mathematical physics of Hubble's Law says, in plain language, is that the greater distance between any two spacetime points in the universe, the faster they recede from each other no matter where located in the cosmos. And the amazing thing of this proposition is that not only is the universe exponentially expanding from any given spacetime point reaching towards an imaginary cosmic horizon, but that the furthest distance between any two hypothetically imaginary entities ( universe event horizon vs. spacetime point, etc. ) will always be no greater than approximately 15 Gly or billion lightyears moving away from each other at the universally constant speed of light! This Hubble's Law fact will be true for all eternity!
As a result, therefore, there is no escape from the universe in which we reside beyond a constant distance of ≈15 Gly or billion lightyears no matter from where we measure distance to the hypothetical ( 2 or 3 dimensional ) cosmic horizon. Furthermore, only spacelike electromagnetic signals can ever reach us from the other side of that hypothetical cosmic horizon. While examining Minkowski's "light cone" ( see: http://www.relativitycalculator.com/Minkowski_special_relativity_geometry.shtml ), this other realm being beyond the hypothetical cosmic horizon is called "Elsewhere" having a spacelike metric, if you recall. Even more depressingly, most of the universe will forever be beyond our empirical grasp for even theoretical examination!
On the other hand, if we think about ourselves as residing in the visible universe as we might conceive of ourselves onboard an oceangoing ship where we can only physically observe to the furthest extent of the far distant horizon, do we assume that that is all there is to the ocean and nothing beyond the horizon's edge? Of course not as we now understand that there's more ocean without exactly [  i.e. epistemologically  ] knowing actually what's on or beneath it in the sense of engaging the naïve reality of our 5 senses. But, nevertheless, there are ocean waves washing onto our side of the horizon from beyond for which we still may be able to discern the nature of the ocean beyond the fixed, visible watery horizon. Likewise, there are visible light spectrum rolling into our timelike realm from the spacelike "reality" beyond. And this will be especially true as the ocean of space inexorably expands at an accelerating pace. So from this we may come to realize that some spacelike light may become blueshifted ( versus redshifted! ) as these light spectrum come rolling into our visible realm on this observable side of the event horizon of our known universe.
But could these "newly" reborn spacelike light coming to our view as observable timelike light at the horizon's visible edge be older than ≈15 Gly or billion years residing at some ≈15 Gly or billion lightyears distance away? The seemingly contradictory answer is yes owing to the physical possibility that that "newly" reborn spacelike light in addition to some multitude of other ancient light closer in could have been sloshing around on this observable side of the universe's event horizon for some times considerably greater than ≈15^{+} billions of years!
Understanding that the original light coming into our visible horizon of sky began from the big bang distance of ≈13.8 [ to upper range ≈15 ] Gly or billion lightyears, the inflationary expanding universe produces redshifted ( stretched! ) light with an appearance upwards of z=1089^{+}, setting c=1 for geometrized units, thereby equivalently obtaining some ≈100^{+} billion lightyears distance away for an evolving observable horizon of sky!
Epoch Timeline ( Galaxy, Star, etc. ) 
z ( redshift ) 
lighttravel distance ( time ) 
proper distance ( universe expansion ) 


Big Bang  1,100  ≈13.77 billion years  ≈13.77 billion lightyears  
CMB (Cosmic Microwave Background) 
1,089 ±1^{[a]}  4.345 x 10^{17} secs ^{[c]}  13,769,621,000 lightyears (13.77 Gly  379,000 ^{[e]} lightyears) 

GNz11 (Earliest Galaxy) 
11.09  ≈ 13.4 billion years (4.1 billion parsec) 
≈ 32 billion ly ( accounting for universe expansion! ) 

Earth  0.00  0.00 secs    
Andromeda ( M31 )  −0.001001 ^{[b]}  8.016 x 10^{13} secs ^{[d]}  2.54 ± 0.11 Mly  

Further, does the ontology of our physical reality allow for an understandable distinction between "objective reality" versus "virtual reality"? Simply stated: 'Appearance vs. Reality'? How do we know the differences without going beyond into untestable metaphysics? [ metaphysics by definition is untestable. yes. ]
Now think about these couple of examples of virtual realities: television and the movies are the most obvious. Your computer screen is a projection of sundry virtual realities. But these examples of virtual realities don’t belong as part of any metaphysics. So we can easily make that distinction. However, what’s a bit more difficult is to separate socalled "objective reality" from virtual reality. Could be in some circumstances that virtual realities are in and of themselves an "objective reality" if the context of those circumstances are thoroughly understood. Yes.
Finally, this all sounds like our human intelligence is existentially living inside a black hole! And by associating this idea with the 'holographic principle' as just presented, it could theoretically be accepted as part of the mathematical physics of both black holes and the universe, that our human perception of 3dimensional reality ( or Einstein's 4 dimensions ) is coming into our minds as a 2dimensional flat projection of ( quantum physics ) reality impinged upon the furthest extent of the cosmic horizon in much the same manner that 2dimensional holograms appear to our brains as a 3 dimensional reality! Why not? Analogous as to how local inertias of bodies are causally predetermined by the furthest distributions of masses of bodies of matter in the cosmos per Ernst Mach's Principle which Einstein accepted as philosophically foundational to his general relativity theory for accelerations and, hence, gravity by Einstein's 'Principle of Equivalence'!
To emphasize: Suppose that we indeed are actually and existentially living inside a Black Hole Universe. Some of the mathematics of Jacob Bekenstein and Stephen Hawking go in that direction. Again, it's called the 'holographic principle'. That what we perceive is actually a hologram of lowerdimensional information imposed upon, spread out against, the furtherest extent of the event horizon of the universe itself!! Never mind an event horizon of a given black hole; now start thinking and speaking of an event horizon of the entire, much greater cosmos itself!!! In this newer way of defining ontological reality, we should mathematically, physicswise, understand the virtual reality of the hologram of the black hole in which we exist and therefore brings into our eyes 3dimensions as opposed to the socalled "objective reality" of the underlying information ( whatever that is! ) impinged on the furtherest extent of the event horizon of the universe itself. Ha! Hence, Plato's 'Appearance vs. Reality' allegory!!
Weird stuff, true. Extremely weird stuff, in fact.
But still, always go back to e=mc2 which arises from the 'relativity of time'. Then there’s the bending of light streams of photons in a gravitational field. The accelerating expansion of the universe. True. Hubble’s Law. [ you know, Hubble’s Space Telescope. ha! ] Oh, the Big Bang! Besides, there is the question of what came before the Big Bang? Why the Big Bang? Now black holes! The event horizons of black holes. The event horizon of the furthest extent of the universe.
All of which severely tests our naïve five senses of reality versus the mathematical physics version of socalled "reality".
And always remember that empirically untestable metaphysic propositions are, by definition, simply statements of faith inspired by personal human inadequacies and emotions incapable of explaining external physical reality since metaphysics is disconnected from either positivistic logic ( the scientific method of empiricism ) or predictive mathematical physics.
Philosophic Inquiry for the Human Condition for Knowing: A Redux
Here's one last item to ponder: if the speed of light was instantaneous and not at a given finite speed, we humans could then "know" everything about everything instantaneously from the light that comes into our eyes! We humans would be instantaneously connected to the furthest parts of the cosmos in our knowledge of what transpires in the cosmos. Nothing would be hidden from either our view or our knowledge of the universe. But this is not true. In fact, we intelligent beings live in a "light cone of knowing" due to the fact that the speed of light is finite, even though at a universal constant.
Actually to be strictly solipsistic, we humans exist  or rather glide along  precisely on this 45^{°} "Lightlike Space" worldline!! [ note: we humans live in a 45  degree "light cone of knowing" since that is the maximum angle between any axis of physical reality and the 4th  dimensional axis of time. ] This lightlike space metric provides us with "Proper Time". And any ideas of "future" or "past" is strictly an invention of the human mind!! Which is ok since it allows us humans to manipulate the external physical and time ( spacetime ) world to the greater benefit of our own species survival.
More philosophically, our human perceptions of external reality can tell us only a limited amount of truth regarding the external world. At a deeper level of understanding, therefore, it is only by means of philosophic and mathematical inquiry that an observer in and can relate their "experiences" to each other beyond what their immediate respective naïve perceptions will tell them. To the observer in there is one sort of angle of velocity motion but to the other observer in there is another, but different, angle of velocity motion, whereas neither would realize that their respective angle of velocity motion differs from the other except by a deeper noumenon of philosophic and mathematical inquiry.
Finally, perceive this simple fact of human existence this way: there are all sorts of magnetic and electric fields around us, practically all the time. But we only "know this" by turning on a television or radio in order "to know" this reality. Otherwise, we humans "know" very, very little about what surrounds us and, in truth, what affects us! Until we turn on the radio or television!! Analogously, this could also be true as regards black holes and the holographic principle for the human understanding of 3dimensional reality!!
So, admittedly, we humans as intelligent beings cannot "know" everything around ourselves at all times and for all places in the universe.
source: http://www.relativitycalculator.com/Minkowski_special_relativity_geometry.shtml; also: http://www.relativitycalculator.com/philosophical_meaning.shtml
Ring of Fire: First Ever Black Hole Image Captured  April 10, 2019
Larger than our entire Solar System, this monster super massive black hole was found in galaxy M87 300 million trillion miles away!
"Beauty is the splendor of truth"  S. Chandrasekhar ( IndianAmerican astrophysicist, 1910  1995, Punjab, British India )
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