[Paper Review] Counterexamples to strong cosmic censorship in asymptotically flat black hole spacetimes

Kyriakos Destounis, R. D. B. Fontana+1 more|arXiv (Cornell University)|Jun 1, 2020

Cosmology and Gravitation Theories1 citations

TL;DR

This paper presents the first robust numerical evidence of counterexamples to the strong cosmic censorship conjecture in asymptotically flat black hole spacetimes by analyzing linear scalar field perturbations on accelerating, charged black holes. It demonstrates that Cauchy horizons can remain stable under certain conditions, particularly near extremality, and identifies quasinormal modes as key to this stability, challenging the long-held belief that mass-inflation singularities always form beyond Cauchy horizons.

ABSTRACT

The extendibility of spacetime and the existence of weak solutions to the Einstein field equations beyond Cauchy horizons, is a crucial ingredient to examine the limits of General Relativity. The strong cosmic censorship conjecture serves as a firewall for gravitation by demanding inextendibility of spacetime beyond the Cauchy horizon. For asymptotically flat spacetimes, the predominance of the blueshift instability and the subsequent formation of a mass-inflation singularity at the Cauchy horizon have, so far, substantiated the conjecture. Here, nevertheless, by considering linear scalar field perturbations on accelerating black holes, we provide, for the first time, robust numerical evidence of counterexamples to strong cosmic censorship in asymptotically flat black hole spacetimes. In particular, we show that the stability of Cauchy horizons in accelerating charged black holes is connected to quasinormal modes, we discuss the regularity requirement for which weak solutions to the field equations can exist at the Cauchy horizon and show that the conjecture may be violated near extremality.

Motivation & Objective

• To investigate the validity of the strong cosmic censorship conjecture in asymptotically flat black hole spacetimes.
• To examine the stability of Cauchy horizons beyond which spacetime may be extendible.
• To determine whether weak solutions to the Einstein field equations can exist at the Cauchy horizon under specific conditions.
• To explore the role of quasinormal modes in the stability of Cauchy horizons in accelerating, charged black holes.
• To assess the conditions under which the strong cosmic censorship conjecture may be violated, particularly near extremality.

Proposed method

• Numerical simulation of linear scalar field perturbations on accelerating black hole spacetimes.
• Analysis of the behavior of the metric and curvature invariants near the Cauchy horizon.
• Investigation of quasinormal mode structure to assess the stability of the Cauchy horizon.
• Evaluation of the regularity conditions required for weak solutions to the Einstein field equations at the Cauchy horizon.
• Comparison of perturbation growth rates and blueshift instabilities in relation to extremal limits.
• Use of numerical relativity techniques to probe the extendibility of spacetime beyond the Cauchy horizon.

Experimental results

Research questions

• RQ1 Can Cauchy horizons in accelerating, charged black holes remain stable under linear scalar field perturbations?
• RQ2 To what extent do quasinormal modes influence the stability of the Cauchy horizon in these spacetimes?
• RQ3 Under what conditions can weak solutions to the Einstein field equations exist at the Cauchy horizon?
• RQ4 Is the strong cosmic censorship conjecture violated near the extremal limit of accelerating black holes?
• RQ5 How does the blueshift instability affect the formation of mass-inflation singularities in these configurations?

Key findings

• Robust numerical evidence shows that Cauchy horizons in accelerating, charged black holes can remain stable under linear scalar field perturbations.
• The stability of the Cauchy horizon is strongly influenced by the structure of quasinormal modes in the system.
• Weak solutions to the Einstein field equations can exist at the Cauchy horizon when regularity conditions are satisfied.
• The strong cosmic censorship conjecture may be violated near the extremal limit of accelerating black holes.
• The absence of mass-inflation singularities in these configurations challenges the prevailing view of inevitable spacetime inextendibility beyond Cauchy horizons.
• The results indicate that the interplay between blueshift effects and quasinormal mode dynamics determines whether the Cauchy horizon remains regular or collapses into a singularity.