Question

Which of these metrics describes a static black hole?

Which of these metrics describes a static black hole? ds? = -cºdť +a? (t) (dx? + dy? + dz2) ds? = a? (n) [-dn? + dr2 + m2 do? + po2 sin? bd62] ds? = - (1+2GM) cºdť? + dx2 + dy2 + dz2 ds2 = – cºdť? + dx? + dy? + dz2 O 2GNM 2 P + dp2 1-2G1M tp2d02 vtp2d02 + p2 sinº Od62 2.

The Hawking temperature of a Schwarzschild black hole is given by

$LaTeX: T_H = \frac{\hbar c^3}{8\pi G_NMk_B}$T H = ℏ c 3 8 π G N M k B.

What is the Hawking temperature for a black hole with the mass of the Sun?

Answer 1

1) I am not really based on the options given but I think last option is correct. This is the metric for non charged static black hole.

------------------------------------

2) In Hawking temperature equation, we have a lot of constants

h is reduced planck's constant = 1.054e-34 J.m

G is gravitational constant = 6.67e-11 N.m² / kg²

c is speed of light = 3e8 m/s

k_B is Boltzmann constant - 1.38e-23 J/K

so,

T_h = 1.054e-34 * 3e8³ / 8 $\pi$ * 6.67e-11 * 1.38e-23 * M

T_h = 1.23e23 / M

as it is given that M = mass of sun = 2e30 Kg

T_h = 6.17e-8 K