Analytical solution of Brill waves

TL;DR

This paper presents an analytical solution for axially symmetric vacuum gravitational waves, revealing conditions under which apparent horizons form in high-amplitude cases, advancing understanding of gravitational wave structures.

Contribution

It introduces a new class of analytical solutions for axially symmetric vacuum initial data with a conformally flat active region and horizon formation at high amplitudes.

Findings

Existence of a conformally flat active region in the solution

Formation of apparent horizons at higher wave amplitudes

Analytical characterization of gravitational wave initial data

Abstract

A class of analytical solutions of axially symmetric vacuum initial data for a self-gravitating system has been found. The active region of the constructed gravitational wave is a thin torus around which the solution is conformally flat. For higher values of gravitational wave amplitude the resulting hypersurface contains apparent horizons.