The dynamics of apparent horizons in Robinson-Trautman spacetimes

TL;DR

This paper introduces a spectral method for locating apparent horizons in Robinson-Trautman spacetimes, analyzing their evolution for different initial data and discussing implications for black hole thermodynamics.

Contribution

It presents a novel spectral approach to find apparent horizons and studies their evolution in Robinson-Trautman spacetimes with various initial conditions.

Findings

Observed a mass gap between final Bondi and apparent horizon masses.

Analyzed horizon evolution for spheroids and black hole collisions.

Discussed thermodynamic implications of mass gaps.

Abstract

We present an alternative scheme of finding apparent horizons based on spectral methods applied to Robinson-Trautman spacetimes. We have considered distinct initial data such as representing the spheroids of matter and the head-on collision of two non-rotating black holes. The evolution of the apparent horizon is presented. We have obtained in some cases a mass gap between the final Bondi and apparent horizon masses, whose implications were briefly commented in the light of the thermodynamics of black holes.