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

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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.

Link to Ashoke Sen's recent paper: arxiv.org/abs/1205.0971

This post imported from StackExchange Physics at 2014-03-17 03:21 (UCT), posted by SE-user Qmechanic
Huh, interesting... I have not heard of this correction term before.

This post imported from StackExchange Physics at 2014-03-17 03:21 (UCT), posted by SE-user David Z
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.

This post imported from StackExchange Physics at 2014-03-17 03:21 (UCT), posted by SE-user Dilaton
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.

This post imported from StackExchange Physics at 2014-03-17 03:21 (UCT), posted by SE-user Siva