Horizons and Geodesics of Black Ellipsoids

TL;DR

This paper investigates the horizon and geodesic properties of black ellipsoid solutions in vacuum Einstein gravity, showing that small deformations lead to geodesic behavior similar to Schwarzschild black holes and proposing black ellipsoid objects.

Contribution

It introduces exact off-diagonal vacuum solutions with ellipsoid symmetry and analyzes their maximal extensions and geodesic structures, revealing potential black ellipsoid configurations.

Findings

Small eccentricity deformations preserve Schwarzschild-like geodesics

Constructed maximal analytic extensions and Penrose diagrams for these metrics

Proposed vacuum static and stationary black ellipsoid solutions

Abstract

We analyze the horizon and geodesic structure of a class of 4D off--diagonal metrics with deformed spherical symmetries, which are exact solutions of the vacuum Einstein equations with anholonomic variables. The maximal analytic extension of the ellipsoid type metrics are constructed and the Penrose diagrams are analyzed with respect to adapted frames. We prove that for small deformations (small eccentricities) there are such metrics that the geodesic behaviour is similar to the Schwarzcshild one. We conclude that some vacuum static and stationary ellipsoid configurations may describe black ellipsoid objects.