1

Could somebody help guide the thinking in this situation?

Do the corrections to entropy $S$, like those of https://arxiv.org/abs/hep-th/0111001, affect the temperature of a black hole, or its mass, or both, or neither?

The Schwarzschild black hole entropy $S_{BH}$ with logarithmic corrections is given by $$ S_{BH} = S_0 + (3/2) \ln S_0 $$ where $S_0= (c^3 A) / (4G\hbar )$ is the Bekenstein Hawking entropy, and $A$ the area of the black hole.

So the question is: is there also a logarithmic correction to mass (energy) or to temperature of the black hole? Why or why not?

The entropy of a black hole is thus not given exactly by "one quarter of the area". There are logarithmic corrections to that statement. The question is:

(1) Is the mass of a black hole exactly "proportional to its radius", or are there logarithmic corrections to this statement?

(2) Is the temperature of a black hole exactly "inversely proportional to its radius" or are there logarithmic corrections to this statement?

Qmechanic
  • 220,844
frauke
  • 704

1 Answers1

-1

It seems that the answer is that only entropy has logarithmic corrections. Neither energy nor temperature has such corrections. The logarithmic corrections of entropy are due to statistical fluctuations. These fluctuations have no effect on temperature or mass/energy.

frauke
  • 704