Answer to Question #90284 in Astronomy | Astrophysics for Shivam Nishad

Question

What is a black hole ? Derive an expression for Schwarzs child radius of a black hole on the basis of Newtonian mechanics and explain its significance.

Answer 1

Black hole is a volume of space where gravity is extreme enough to prevent the escape of even the fastest moving particles. The name 'black' hole because Not even light can break free

The principle of conservation of energy to a photon emitted from a star of mass M

$$\frac {mv^2}{2}=\frac {GMm}{r} (1)$$

where m denotes the equivalent mass of a photon

If in equation the velocity v of a photon with the speed of light c then we rewriter (1) as

$$\frac {c^2}{2}=\frac {GM}{r} (2)$$

The Schwarzschild radius is given as

$$r=\frac {2GM}{c^2} (3)$$

In 1783, John Mitchell derived the correct formula for the Schwarzschild radius. However, we must emphasize that, despite the correctness of the above result, Mitchell's formulation was wrong and it should not be considered the proof of the formula of the Schwarzschild radius for black holes. If we want to obtain a correct derivation of this formula we should use either GR, quantum gravity or the Planck units (an extremely primitive form of quantum gravity).