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Cosmological production of charged black hole pairs

R. B. Mann, S. F. Ross

TL;DR

The paper analyzes the cosmological production of charged black hole pairs in a de Sitter background using instanton techniques. It shows that removing conical singularities in the charged C metric with Λ>0 necessarily reduces to Reissner–Nordström–de Sitter, and it constructs four RN–dS instantons (lukewarm, cold, charged Nariai, ultracold) corresponding to non-extreme and extreme pair creation, with actions yielding suppressed rates relative to pure de Sitter. A central result is that the pair-creation entropy equals one quarter of the total horizon area, and extreme BH pairs are suppressed by e^{S_bh}, mirroring the Ernst instantons in electromagnetic backgrounds. The Type I instanton in the zero-Λ limit is identified as the RN solution, reinforcing connections between these gravitational instantons and KK/vacuum decay processes, and suggesting robustness of these effects in quantum gravity.

Abstract

We investigate the pair creation of charged black holes in a background with a positive cosmological constant. We consider $C$ metrics with a cosmological constant, and show that the conical singularities in the metric only disappear when it reduces to the Reissner-Nordström de Sitter metric. We construct an instanton describing the pair production of extreme black holes and an instanton describing the pair production of non-extreme black holes from the Reissner-Nordström de Sitter metric, and calculate their actions. There are a number of striking similarities between these instantons and the Ernst instantons, which describe pair production in a background electromagnetic field. We also observe that the type I instanton in the ordinary $C$ metric with zero cosmological constant is actually the Reissner-Nordström solution.

Cosmological production of charged black hole pairs

TL;DR

The paper analyzes the cosmological production of charged black hole pairs in a de Sitter background using instanton techniques. It shows that removing conical singularities in the charged C metric with Λ>0 necessarily reduces to Reissner–Nordström–de Sitter, and it constructs four RN–dS instantons (lukewarm, cold, charged Nariai, ultracold) corresponding to non-extreme and extreme pair creation, with actions yielding suppressed rates relative to pure de Sitter. A central result is that the pair-creation entropy equals one quarter of the total horizon area, and extreme BH pairs are suppressed by e^{S_bh}, mirroring the Ernst instantons in electromagnetic backgrounds. The Type I instanton in the zero-Λ limit is identified as the RN solution, reinforcing connections between these gravitational instantons and KK/vacuum decay processes, and suggesting robustness of these effects in quantum gravity.

Abstract

We investigate the pair creation of charged black holes in a background with a positive cosmological constant. We consider metrics with a cosmological constant, and show that the conical singularities in the metric only disappear when it reduces to the Reissner-Nordström de Sitter metric. We construct an instanton describing the pair production of extreme black holes and an instanton describing the pair production of non-extreme black holes from the Reissner-Nordström de Sitter metric, and calculate their actions. There are a number of striking similarities between these instantons and the Ernst instantons, which describe pair production in a background electromagnetic field. We also observe that the type I instanton in the ordinary metric with zero cosmological constant is actually the Reissner-Nordström solution.

Paper Structure

This paper contains 7 sections, 120 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Cosmological $C$ metrics
  3. The Type I instanton
  4. Reissner-Nordström de Sitter instantons
  5. Pair creation rate and entropy
  6. Conclusions
  7. Acknowledgements

Figures (3)

  • Figure 1: The values of $Q$ and $M$ for which instantons can be obtained in the cosmological case. The plot is of the dimensionless quantities $Q\sqrt{\Lambda}$ vs. $M\sqrt{\Lambda}$. The curve DU represents the cold solutions, DC represents the lukewarm solutions, and NU represents the charged Nariai solutions. The point at D is de Sitter space, while U is the ultracold case, and N is the Nariai solution.
  • Figure 2: The values of $Q$ and $M$ for which instantons can be obtained in the electromagnetic case. The plot is of the dimensionless quantities $q A$ vs. $m A$. The curve OA represents the extreme solutions, OC represents the lukewarm solutions, and BA represents the Type I instantons. The point at O is the Melvin solution.
  • Figure 3: The action for the various instantons in the cosmological case. The action as a fraction of the action for de Sitter space, $I/I_{\rm de\ Sitter}$, is plotted against the dimensionless mass $M\sqrt{\Lambda}$. The curve DU1 represents the cold solutions, DC represents the lukewarm solutions, and NU represents the charged Nariai solutions. The point at D is de Sitter space, N is the Nariai solution, and U1 and U2 represent the actions of the first and second type of ultracold solutions. Note that U does not correspond to one of the ultracold solutions.