Cauchy-characteristic matching

TL;DR

This paper introduces a new algorithm combining Cauchy and characteristic methods for numerically solving Einstein's equations, enabling better simulation of gravitational phenomena like black hole collisions.

Contribution

It presents a pedagogic overview of a hybrid approach that integrates Cauchy and characteristic hypersurfaces for improved numerical relativity simulations.

Findings

Effective in simplified test problems

Used to develop 3-D black hole collision simulations

Combines strengths of two leading computational approaches

Abstract

This paper gives a detailed pedagogic presentation of the central concepts underlying a new algorithm for the numerical solution of Einstein's equations for gravitation. This approach incorporates the best features of the two leading approaches to computational gravitation, carving up spacetime via Cauchy hypersurfaces within a central worldtube, and using characteristic hypersurfaces in its exterior to connect this region with null infinity and study gravitational radiation. It has worked well in simplified test problems, and is currently being used to build computer codes to simulate black hole collisions in 3-D.