Perturbations and Stability of Black Ellipsoids

TL;DR

This paper investigates the stability of black ellipsoid solutions in four-dimensional vacuum Einstein equations, demonstrating that small eccentricity deformations of Schwarzschild black holes can be stable under perturbations.

Contribution

It introduces a new class of off-diagonal metrics for black ellipsoids and analyzes their stability using inverse scattering theory.

Findings

Black ellipsoid solutions can be stable under perturbations.

Small eccentricity deformations do not lead to instability.

Perturbation analysis uses Schrödinger equations in a novel context.

Abstract

We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of diagonal metrics. The analysis is performed in the approximation of small eccentricity deformations of the Schwarzschild solution. We conclude that such anisotropic black hole objects may be stable with respect to the perturbations parametrized by the Schrodinger equations in the framework of the one--dimensional inverse scattering theory.