Hawking Radiation

3
0

Main Question or Discussion Point

Hello, I am rather new to Physics and for a class project on exponential growth and decay in nature and I chose the effects Hawking Radiation on black holes. If anyone could help explain how the mass and temperature change over time and how to calculate them(this one especially) that would be wonderful
 

Answers and Replies

3
0
Simplified, why are these decreases(in mass) and increases(in heat) expoenential.
 
3
0
*exponential
 
14
2
how the mass and temperature change over time and how to calculate them
According to the Bekenstein–Hawking formula in black hole thermodynamics, $$S=\frac{kAc^3}{4G\hbar}$$ Consider a Schwarzschild black hole, we know that $$r_{\rm g}=\frac{2GM}{c^2},\ A=4\pi r_{\rm g}^2$$ Therefore, we can get $$M^2=\frac{\hbar c^3}{4\pi k_{\rm B} G}S$$ From thermodynamics, we learn that ##{\rm d}M=T{\rm d}S##, so we have $$T=\frac{{\rm d} M}{{\rm d} S}=\frac{\hbar c^3}{8\pi k_{\rm B}G}\frac{1}{M}$$I believe this is what you want.

By the way, according to the Stefan-Boltzmann law, $$\frac{{\rm d}M}{{\rm d}t}=-\sigma AT^4$$ and thus you can know how the mass and temperature change over time.
 

Related Threads for: Hawking Radiation

Replies
6
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
6
Views
987
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
8
Views
4K
  • Last Post
Replies
5
Views
2K
Top