Gravitational time dilation and black hole

In this article, we derive the gravitational time dilation factor in a new manner, which allows us to identify the mathematical cause of Schwarzschild radius, to give a theoretical way to avoid it and to compute properties of black hole. General relativity effects are computed as simple as in special relativity. Observability of black hole is discussed.

The wonderful work of Karl Schwarzschild describes the spacetime curved by a spherical gravitational field, which agree precisely with observation as shown by the orbital precession of the planet Mercury. In addition, Schwarzschild metric possesses a completely new feature: a critical radius named Schwarzschild radius that marks the lower limit of describable space. This feature is weird because it splits space into 2 regions, the normal space is outside this radius and the region inside it cannot be mathematically defined. This region is called a black hole because no information, not even light, could escape from it.

The funding principle of physics is that the entire universe is governed by physical laws whatsoever. Such weird region out of the reach of physics hints that unknown physical laws are there. So, let us try to understand deeper Schwarzschild radius and find out where it comes from.

Comparison with the time dilation in special relativity
What makes Schwarzschild radius?
Using relativistic transformation of acceleration
Gravitational relativistic dynamics
Below Schwarzschild radius
About black hole, Observational evidences

Figures and equations are in the article below:
Gravitational time dilation and black hole