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?

  • $\begingroup$ Please be specific about “the logarithmic corrections” that you are referring to, such as with a link to a paper. $\endgroup$
    – G. Smith
    Nov 16 '19 at 0:03
  • $\begingroup$ Rather than just adding the link, could you copy the relevant passage and highlight what it is that you are questioning (be specific about what you fathom versus what you don’t) $\endgroup$
    – Kyle Kanos
    Nov 16 '19 at 13:46
  • $\begingroup$ I did as you asked. $\endgroup$
    – frauke
    Nov 16 '19 at 18:03
  • $\begingroup$ I extended the question to make it even clearer. $\endgroup$
    – frauke
    Nov 19 '19 at 4:05
  • $\begingroup$ related : How is the logarithmic correction to the entropy of a non extremal black hole derived? even if I did not consider in my answer the orgin of the log-correction from a Cardy-like perspective. $\endgroup$
    – mmanu F
    Nov 28 '19 at 12:12

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.

  • 1
    $\begingroup$ so, aren't quantum fluctuations that lead to an effective black hole temperature through Bogoliubov transformations? Perhaps it is unexpected that fluctuations have no effect on temperature. What effects are in play to result in the absence of an influence? $\endgroup$
    – lurscher
    Nov 18 '19 at 3:35
  • $\begingroup$ Can you edit the first question and make it clearer? I do not understand the grammar of it. $\endgroup$
    – frauke
    Nov 18 '19 at 4:10
  • $\begingroup$ I downvoted the answer. I will be happy to undo whenever: - some background and definitions will be given (what are those statistical fluctuations, and why only consider these? I know about other sources of log corrections, see my link in the comment above) - the affirmation (no effect on E & T) will be clearly justified (It is unclear for E in the paper you cited, and T isn't and can't be AFAIK studied that way) $\endgroup$
    – mmanu F
    Nov 28 '19 at 17:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.