Two-Sided Gravitational Mirror: Sealing off Curvature Singularities

TL;DR

This paper introduces a novel two-sided gravitational mirror solution that prevents curvature singularities by bouncing all incident null geodesics, offering new insights into non-singular spacetime geometries.

Contribution

It presents the first exact, static, radially symmetric two-sided mirror solution asymptotic to the massless BTZ black hole, demonstrating a new mechanism for sealing off singularities.

Findings

Derives an exact two-sided mirror solution in a BTZ background.

Shows the mirror bounces all incident null geodesics, preventing singularities.

Analyzes the local structure of a massive mirror.

Abstract

A gravitational mirror is a non-singular finite redshift surface which bounces all incident null geodesics. While a white mirror (outward bouncing) resembles 't Hooft's brick wall, a black mirror (inward bouncing) offers a novel mechanism for sealing off curvature singularities. The geometry underlying a two-sided mirror is characterized by a single signature change, to be contrasted with the signature flip which governs the black hole geometry. To demonstrate the phenomenon analytically, we derive an exact, static, radially symmetric, two-sided mirror solution, which asymptotes the massless BTZ black hole background, and then probe the local structure of a massive mirror.