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Introduction to 3+1 Numerical Relativity$
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Miguel Alcubierre

Print publication date: 2008

Print ISBN-13: 9780199205677

Published to Oxford Scholarship Online: September 2008

DOI: 10.1093/acprof:oso/9780199205677.001.0001

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Introduction to 3+1 Numerical Relativity

Miguel Alcubierre

Oxford University Press

Gravitational waves are one of the most important physical phenomena associated with the presence of strong and dynamic gravitational fields, and as such they are of great interest in numerical relativity. There are two main approaches to the extraction of gravitational wave information from a numerical simulation. Traditional approach has been based on the theory of perturbations of a Schwarzschild spacetime developed originally by Regge and Wheeler, Zerilli, and a number of other authors, and later recast as a gauge invariant framework by Moncrief. In recent years, however, it has become increasingly common in numerical relativity to extract gravitational wave information in terms of the components of the Weyl curvature tensor with respect to a frame of null vectors, using what is known as the Newman-Penrose formalism. This chapter presents a brief introduction to both these approaches, and describes how to calculate the energy and momentum radiated by gravitational waves in each case.

Keywords:   gravitational waves, Schwazschild, parity perturbations, gravitational radiation, Weyl tensor, tetrad formalism, invariants, tensors, multipole decomposition

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