Extremal black holes in D=5: SUSY vs. Gauss-Bonnet corrections

TL;DR

This paper compares the effects of supersymmetric and Gauss-Bonnet higher-order corrections on the entropy of five-dimensional extremal black holes, revealing differences for non-BPS solutions and consistency with microscopic entropy in certain cases.

Contribution

It provides a detailed analysis of near-horizon solutions and entropy corrections for 5D extremal black holes with different higher-order terms, including new non-BPS solutions and comparisons with string microstates.

Findings

For large BPS black holes, corrections are similar for both types.

Non-BPS black holes show different entropy corrections depending on the higher-order term.

Gauss-Bonnet corrections yield entropy consistent with microscopic string theory in known cases.

Abstract

We analyse near-horizon solutions and compare the results for the black hole entropy of five-dimensional spherically symmetric extremal black holes when the N=2 SUGRA actions are supplied with two different types of higher-order corrections: (1) supersymmetric completion of gravitational Chern-Simons term, and (2) Gauss-Bonnet term. We show that for large BPS black holes lowest order \alpha' corrections to the entropy are the same, but for non-BPS are generally different. We pay special attention to the class of prepotentials connected with K3\times T^2 and T^6 compactifications. For supersymmetric correction we find beside BPS also a set of non-BPS solutions. In the particular case of T^6 compactification (equivalent to the heterotic string on $T^4\times S^1$) we find the (almost) complete set of solutions (with exception of some non-BPS small black holes), and show that entropy of small black holes is different from statistical entropy obtained by counting of microstates of heterotic string theory. We also find complete set of solutions for K3\times T^2 and T^6 case when correction is given by Gauss-Bonnet term. Contrary to four-dimensional case, obtained entropy is different from the one with supersymmetric correction. We show that in Gauss-Bonnet case entropy of small ``BPS'' black holes agrees with microscopic entropy in the known cases.