On Attractor Mechanism and Entropy Function for Non-extremal Black Holes/Branes

TL;DR

This paper investigates the applicability of the entropy function formalism to non-extremal black branes, demonstrating that despite the absence of an attractor mechanism, the formalism accurately computes entropy at saddle points.

Contribution

It shows that the entropy function formalism remains valid for non-extremal black branes, extending its use beyond extremal cases.

Findings

Entropy function formalism applies to non-extremal D3, M2, M5-branes.

Entropy is obtained from the entropy function at its saddle point.

The attractor mechanism is absent in non-extremal black holes/branes.

Abstract

We examine in details the entropy function formalism for non-extremal D3, M2, and M5-branes that their throat approximation is given by Schwarzschild black hole in AdS_{p+2} \times S^{D-(p+2)}. We show that even though there is no attractor mechanism in the non-extremal black holes/branes, the entropy function formalism does work and the entropy is given by the entropy function at its saddle point.