A C-Function For Non-Supersymmetric Attractors

TL;DR

This paper introduces a c-function applicable to four-dimensional gravity theories with gauge fields and moduli, which decreases monotonically and equals black hole entropy at the horizon, covering both extremal and non-extremal cases.

Contribution

It proposes a new c-function for non-supersymmetric black holes that applies to both extremal and non-extremal solutions in four-dimensional gravity theories.

Findings

The c-function decreases monotonically from infinity to the horizon.

At the horizon, the c-function equals the black hole entropy.

The approach extends to higher dimensions and p-form gauge fields.

Abstract

We present a c-function for spherically symmetric, static and asymptotically flat solutions in theories of four-dimensional gravity coupled to gauge fields and moduli. The c-function is valid for both extremal and non-extremal black holes. It monotonically decreases from infinity and in the static region acquires its minimum value at the horizon, where it equals the entropy of the black hole. Higher dimensional cases, involving $p$-form gauge fields, and other generalisations are also discussed.