Question

As our Sun ages, it will go through a period of collapse. If we take the maximum possible density of any material in the universe to be that of neutron stars which have densities around 1017kg/m3, is it possible that our sun could collapse to form a black hole? What is the minimum mass of an object that could potentially form a black hole if it collapses to have the same density as a neutron star? (express your answer as a multiple of the solar mass)

Answer 1

-Any mass can become a black hole if it collapses down to the Schwarzschild radius.

Let's calculate the Schwarzschild radius for Sun to decide if it can become a black hole

R_s ( Schwarzschild radius for Sun) = 3 km ( i checked the value with wiki)

Radus of sun = 696,000 km

Any object with a physical radius smaller than its Schwarzschild radius will be a black hole., therefore Sun cannot be a black hole.

b) For an object to be black hole. it's radius must be less than Schwarzschild radius.

R_s = 2GM/ R^2

As we are assuming that neutron star has become the black hole, therefore it's radis will become equal to Schwarzschild radius.

R_s = 2GM/ C^2

R_s = 2GM/C^2----------eq!1)

density = mass /volume

10^17 = M/ ( 4/3 R^3)

10^17 = (3M/ 4​ R^3)----------eq(2)

using eq(1) and (2) , we get

10^17 = r^3

plugging the value of r from eq(1)

10^17 = ( 2GM/C^2)^3

colving for mass = 8.56 x 10^15 kg apprx

solar mass= 1.989x 10^30 kg

mass of neutron star = 4.3 x 10^-15 times solar mass