Penrose Inequality for Gravitational Waves

TL;DR

This paper numerically constructs axially symmetric vacuum initial data with apparent horizons and confirms they satisfy the Penrose inequality, supporting its validity for both massive and source-free gravitational systems.

Contribution

It provides the first numerical evidence that axially symmetric vacuum solutions with apparent horizons obey the Penrose inequality.

Findings

Solutions satisfy the Penrose inequality

Supports the conjecture for massive and source-free systems

Numerical construction of initial data with apparent horizons

Abstract

We investigate axially symmetric asymptotically flat vacuum self-gravitating system. A class of initial data with apparent horizon was numerically constructed. The examined solutions satisfy the Penrose inequality. The prior analysis of a massive system and the present results suggest that either massive or sourcefree configurations fulfill the Penrose inequality.