# Do the logarithmic corrections to black hole entropy imply corrections to their energy or temperature?

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?

• Please be specific about “the logarithmic corrections” that you are referring to, such as with a link to a paper. – G. Smith Nov 16 '19 at 0:03
• 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) – Kyle Kanos Nov 16 '19 at 13:46
• I did as you asked. – frauke Nov 16 '19 at 18:03
• I extended the question to make it even clearer. – frauke Nov 19 '19 at 4:05
• 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. – mmanu F Nov 28 '19 at 12:12