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?