Prolate horizons and the Penrose inequality

TL;DR

This paper explores non-spherical, non-rotating black holes with non-zero extrinsic curvature, constructing initial data that can violate the Penrose inequality and analyzing energy condition violations.

Contribution

It introduces a method to construct initial data for prolate black holes with non-zero extrinsic curvature, challenging the Penrose inequality.

Findings

Penrose inequality can be violated with prolate black holes.

Dominant energy condition is violated at the poles.

Initial data construction allows for horizon placement flexibility.

Abstract

The Penrose inequality has so far been proven in cases of spherical symmetry and in cases of zero extrinsic curvature. The next simplest case worth exploring would be non-spherical, non-rotating black holes with non-zero extrinsic curvature. Following Karkowski et al.'s construction of prolate black holes, we define initial data on an asymptotically flat spacelike 3-surface with nonzero extrinsic curvature that may be chosen freely. This gives us the freedom to define the location of the apparent horizon such that the Penrose inequality is violated. We show that the dominant energy condition is violated at the poles for all cases considered.