On the Entropy of Four-Dimensional Near-Extremal N=2 Black Holes with R^2-Terms

TL;DR

This paper derives a generalized entropy formula for near-extremal N=2 black holes with R^2-terms, revealing that the entropy remains unchanged from the extremal case to order mu^2, unlike the charge shift in the non-R^2 case.

Contribution

It introduces a new Wald entropy formula for non-extremal N=2 black holes with R^2-terms and constructs specific near-extremal solutions showing unchanged entropy to order mu^2.

Findings

Entropy matches extremal case to order mu^2

R^2-terms eliminate charge shift behavior

Constructed near-extremal horizon solutions

Abstract

We consider the entropy of four-dimensional near-extremal N=2 black holes. Without R^2-terms, the Bekenstein-Hawking entropy formula has the structure of the extremal black holes entropy with a shift of the charges depending on the non-extremality parameter and the moduli at infinity. We derive a generalized Wald entropy formula for non-extremal N=2 black holes with R^2-terms. We construct a class of small near-extremal horizon solutions with R^2-terms. In this case the entropy is the same as in the extremal case to order O(mu^2), and does not exhibit the charge shift behavior.