Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

TL;DR

This paper calculates quantum logarithmic corrections to the entropy of various extremal black holes in four and five dimensions, confirming string theory results for supersymmetric cases and testing microscopic models for non-supersymmetric ones.

Contribution

It provides a comprehensive computation of logarithmic entropy corrections for rotating extremal black holes using quantum gravity, including both supersymmetric and non-supersymmetric cases, and compares with microscopic theories.

Findings

Logarithmic corrections match string theory predictions for BMPV black holes.

Correct dependence on gauge fields and angular momentum in corrections.

Highlights limitations of the Cardy limit for certain black holes.

Abstract

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.