Hyperboloidal data and evolution

TL;DR

This paper explores hyperboloidal evolution in general relativity, constructing initial data, analyzing horizons, and applying conformal field equations and toy models to understand numerical and theoretical aspects.

Contribution

It introduces new numerical methods for hyperboloidal initial data, applies Friedrich's conformal equations, and investigates continuum instabilities in Maxwell equations.

Findings

Constructed hyperboloidal Brill wave initial data

Performed systematic apparent horizon search

Applied conformal field equations to Schwarzschild-Kruskal spacetime

Abstract

We discuss the hyperboloidal evolution problem in general relativity from a numerical perspective, and present some new results. Families of initial data which are the hyperboloidal analogue of Brill waves are constructed numerically, and a systematic search for apparent horizons is performed. Schwarzschild-Kruskal spacetime is discussed as a first application of Friedrich's general conformal field equations in spherical symmetry, and the Maxwell equations are discussed on a nontrivial background as a toy model for continuum instabilities.