A numerical study of Penrose-like inequalities in a family of axially symmetric initial data

TL;DR

This paper numerically investigates Penrose-like inequalities in axially symmetric black hole initial data, testing geometric bounds and demonstrating their use in horizon detection algorithms.

Contribution

It introduces a numerical study of Penrose inequalities in a family of axisymmetric initial data, providing insights into their validity and application.

Findings

Penrose inequalities are consistent with the numerical data.

The inequalities can diagnose the presence of apparent horizons.

Numerical methods for horizon finding are improved using these inequalities.

Abstract

Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a stationarity state. In this setting, it follows that the minimal area containing an apparent horizon is bound by the square of the total ADM mass (Penrose inequality conjecture). Following Dain et al. 2002, we construct numerically a family of axisymmetric initial data with one or several marginally trapped surfaces. Penrose and related geometric inequalities are discused for these data. As a by-product, it is shown how Penrose inequality can be used as a diagnosis for an apparent horizon finder numerical routine.