Question

What would happen if the sun suddenly became a black hole without changing its mass?

Answer 1

Answer:

It would shrink to a radius of 2.95 km

Explanation:

In order to be a black hole, the Sun must shrink so that its radius becomes equal to its Schwarzschild radius:

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

where

G is the gravitational constant

$M=1.99\cdot 10^{30} kg$ is the mass of the Sun

c is the speed of light

Substituting into the equation, we find

$r=\frac{2(6.67\cdot 10^{-11}m^3 kg^{-1} s^{-2})(1.99\cdot 10^{30} kg)}{(3\cdot 10^8 m/s)^2}=2950 m=2.95 km$

So, the Sun should shrink to a radius of 2.95 km.