Why Aren't Black Holes Infinitely Produced?

TL;DR

This paper investigates the pair production rate of Reissner-Nordstrom black holes considering their internal states, highlighting the implications of infinite versus finite internal states on the production rate.

Contribution

It reexamines black hole pair production including internal states and proposes that finiteness of these states could resolve the divergence in production rate.

Findings

Pair production rate is proportional to Tr e^{-beta H} over internal states.

Infinite internal states lead to an infinite production rate.

Finiteness of internal states could resolve the divergence issue.

Abstract

Unitarity and locality imply a remnant solution to the information problem, and also imply that Reissner-Nordstrom black holes have infinite numbers of internal states. Pair production of such black holes is reexamined including the contribution of these states. It is argued that the rate is proportional to the thermodynamic quantity Tr e^{-beta H}, where the trace is over the internal states of a black hole; this is in agreement with estimates from an effective field theory for black holes. This quantity, and the rate, is apparently infinite due to the infinite number of states. One obvious out is if the number of internal states of a black hole is finite.