Entropy, Area, and Black Hole Pairs

TL;DR

This paper explores the relationship between black hole entropy and horizon area, showing that extremal black holes have zero entropy despite nonzero horizon area, and linking pair creation rates to horizon areas.

Contribution

It clarifies the connection between gravitational entropy and horizon area, especially for extremal black holes, and relates pair creation rates to horizon areas, providing new insights into black hole thermodynamics.

Findings

Extremal Reissner-Nordstr"om black holes have zero entropy despite nonzero horizon area.

Pair creation rate is related to the areas of acceleration and event horizons.

Black hole annihilation discussion suggests Planck scale remnants can't preserve unitarity.

Abstract

We clarify the relation between gravitational entropy and the area of horizons. We first show that the entropy of an extreme Reissner-Nordstr\"om black hole is $zero$, despite the fact that its horizon has nonzero area. Next, we consider the pair creation of extremal and nonextremal black holes. It is shown that the action which governs the rate of this pair creation is directly related to the area of the acceleration horizon and (in the nonextremal case) the area of the black hole event horizon. This provides a simple explanation of the result that the rate of pair creation of non-extreme black holes is enhanced by precisely the black hole entropy. Finally, we discuss black hole $annihilation$, and argue that Planck scale remnants are not sufficient to preserve unitarity in quantum gravity.