Stability and Instability of the Reissner-Nordstrom Cauchy Horizon and the Problem of Uniqueness in General Relativity

TL;DR

This paper discusses recent mathematical results on the stability of the Reissner-Nordstrom Cauchy horizon and addresses the problem of uniqueness in the Einstein-Maxwell-Scalar Field system within general relativity.

Contribution

It provides a rigorous mathematical analysis of the global behavior and uniqueness of solutions to a characteristic initial value problem in spherical symmetry, advancing understanding of cosmic censorship.

Findings

Global behavior of solutions is fully understood mathematically.

Theorems on the stability and instability of horizons are established.

The problem of uniqueness in the Einstein-Maxwell-Scalar Field system is resolved.

Abstract

This talk describes some recent results [16] regarding the problem of uniqueness in the large (also known as strong cosmic censorship) for the initial value problem in general relativity. In order to isolate the essential analytic features of the problem from the complicated setting of gravitational collapse in which it arises, some familiarity with conformal properties of certain celebrated special solutions of the theory of relativity will have to be developed. This talk is an attempt to present precisely these features to an audience of non-specialists, in a way which will hopefully fully motivate a certain characteristic initial value problem for the spherically-symmetric Einstein-Maxwell-Scalar Field system. The considerations outlined here leading to this particular initial value problem are well known in the physics relativity community, where the problem of uniqueness has been studied heuristically [1, 22] and numerically [2, 3]. In [16], the global behavior of solutions to this IVP, in particular, the issue of uniqueness, is mathematically completely understood. A statement of the relevant Theorems is included in Section 9. Only a sketch of the ideas of the proof is provided here, but the readers may refer to [16] for details.