From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity

TL;DR

This paper reviews the interdisciplinary relationship between mathematical and numerical general relativity, focusing on black hole studies, asymptotic flatness, initial value problems, and geometric inequalities.

Contribution

It highlights recent developments and interactions between mathematical and numerical approaches in understanding isolated systems and black holes in general relativity.

Findings

Advances in the study of black hole horizons

Insights into asymptotic flatness and initial value problems

Discussion of geometric inequalities in relativity

Abstract

This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasi-local black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.