Hot Attractors

TL;DR

This paper demonstrates a universal relation between the areas of horizons in non-extremal black holes, linking it to extremal limits, and provides a microscopic interpretation via conformal field theory.

Contribution

It establishes a new area product relation for non-extremal black holes using thermodynamics and the attractor mechanism, extending extremal black hole results.

Findings

Product of horizon areas equals the square of the extremal horizon area.

Certain vanishing quantities in extremal black holes are zero between horizons.

The relation is supported by analysis of known solutions and CFT duality.

Abstract

The product of the areas of the event horizon and the Cauchy horizon of a non-extremal black hole equals the square of the area of the horizon of the black hole obtained from taking the smooth extremal limit. We establish this result for a large class of black holes using the second order equations of motion, black hole thermodynamics, and the attractor mechanism for extremal black holes. This happens even though the area of each horizon generically depends on the moduli, which are asymptotic values of scalar fields. The conformal field theory dual to the BTZ black hole facilitates a microscopic interpretation of the result. In addition, we demonstrate that certain quantities which vanish in the extremal case are zero when integrated over the region between the two horizons. We corroborate these conclusions through an analysis of known solutions.