# How is the logarithmic correction to the entropy of a non extremal black hole derived?

Ive just read, that for non extremal black holes, there exists a logarithmic (and other) correction(s) to the well known term proportional to the area of the horizon such that

$S = \frac{A}{4G} + K \ln \left(\frac{A}{4G}\right)$

where K is a constant.

How is this logarithmic (and other) correction term(s) derived generally? Or how can I see that there has to be such a logarithmic correction?

Im wondering if there is some kind of a general makroscopic thermodynamic or semiclassical argument (in analogy to some derivations of the first term) that motivates the appearance of the second logarithmic term and does not depend on how the microstates are quantum gravitationally implemented.

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Link to Ashoke Sen's recent paper: arxiv.org/abs/1205.0971 –  Qmechanic May 7 '12 at 21:15
Huh, interesting... I have not heard of this correction term before. –  David Z May 8 '12 at 4:32
Yep @Qmechanic a discussion of this paper is what made me asking this. Basically, I`m wondering if there is some kind of a general makroscopic thermodynamic or semiclassical argument (in analogy to some derivations of the first term) that motivates the appearance of the second logarithmic term and does not depend on how the microstates are quantum gravitationally implemented. –  Dilaton May 8 '12 at 8:32
I think the subleading log corrections (should) depend on the microscopic theory. You might consider those as the predictions that would (in principle) help differentiate between models. –  Siva Mar 21 '13 at 4:00
I wonder what this looks like in non-Planck units. There must be a bunch of constants inside that $\ln$ to make its argument dimensionless, and knowing what they are might give some insight into your question. (I know this is old, but just saying.) –  Nathaniel Jul 6 at 6:33

## 1 Answer

Christoph Schiller argues that the log term arises from the different orientations that a black hole can have in space. His proposal also fixes the value of the constant K, as he explains, to 3/2 times the Boltzmann constant k_B.

I found this in the section "Entropy of horizons" on page 269 and 270 of "The strand model - a speculation on unification". I downloaded the pdf from http://www.motionmountain.net/research.html

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