This compilation of Einstein's gravity equations includes the following along with ancillary backups:
1). The Geodesic Spacetime Equation which simply states that the shortest distance an object travels thru space is that which effectively expends the least amount of energy in going thru a gravity field of varying intensities;
2). The Null Geodesic is identical to the path travelled by a beam of light as it curves around any body of mass producing a gravity field. This is the simplest way to understand this idea, actually no big deal at all;
3). Of course, Einstein's ( EFE <==> Einstein Field Equation ) Gravity Field Equation. Here are all the steps without any gaps unlike what you might otherwise expect in other GR texts. Not always easy but plenty of diagrams to move you along the mathematics. Just expand your own imaginations here. Einstein's EFE idea is really very simple and philosophical. It's just the math which gets hairy. Ha!;
4). Finally, the Schwarzschild Gravity Equation is developed from which directly comes the so-called 'Schwarzschild radius' which is no more than the imaginary spherical boundary delineating escape velocity bounds such as here in the upper levels of our own Earth's gravity field. This now profoundly forms the basis for understanding black holes and their 'event horizons'!! It is really that simple. Yes. But necessary.
In fact, once you start to ponder black holes, it may be that we all are living inside an in-out black hole of multiple universes! Some of the mathematics point in that direction. It does so in order to preserve the fundamental physics idea of conservation of mass-energy and information where we learn about Hawking ( and Beckenstein! )'s radiation and so forth.
