Numerical Relativity at the Frontier

TL;DR

Numerical relativity has advanced significantly with new algorithms enabling detailed simulations of complex astrophysical phenomena, aiding in gravitational wave research and fundamental physics insights.

Contribution

The paper reviews recent developments in numerical relativity, emphasizing new algorithms and their applications to astrophysical systems and fundamental questions.

Findings

Successful simulation of black hole and neutron star mergers

Insights into critical phenomena and cosmic censorship

Enhanced interpretation of gravitational wave data

Abstract

Numerical relativity is an essential tool for solving Einstein's equations of general relativity for dynamical systems characterized by high velocities and strong gravitational fields. The implementation of new algorithms that can solve these nonlinear equations in 3+1 dimensions has enabled us to tackle many long-standing problems of astrophysical interest, leading to an explosion of important new results. Numerical relativity has been used to simulate the evolution of a diverse array of physical systems, including coalescing black hole and neutron star binaries, rotating and collapsing compact objects (stars, collisionless clusters, and scalar fields), and magnetic and viscous stars, to name a few. Numerical relativity has been exploited to address fundamental points of principle, including critical phenomena and cosmic censorship. It holds great promise as a guide for interpreting observations of gravitational waves and gamma-ray bursts and identifying the sources of such radiation. Highlights of a few recent developments in numerical relativity are sketched in this brief overview.