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Gravitational WavesVolume 1: Theory and Experiments$
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Michele Maggiore

Print publication date: 2007

Print ISBN-13: 9780198570745

Published to Oxford Scholarship Online: January 2008

DOI: 10.1093/acprof:oso/9780198570745.001.0001

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1 The geometric approach to GWs

1 The geometric approach to GWs

Chapter:
(p.3) 1 The geometric approach to GWs
Source:
Gravitational Waves
Author(s):

Michele Maggiore

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198570745.003.0001

This chapter discusses how gravitational waves emerge from general relativity, and what their properties are. The most straightforward approach is ‘linearized theory’, where the Einstein equations are expanded around the flat Minkowski metric. It is shown how a wave equation emerges and how the solutions can be put in an especially simple form by an appropriate gauge choice. Using standard tools of general relativity such as the geodesic equation and the equation of the geodesic deviation, how these waves interact with a set of test masses is detailed. The energy and momentum carried by GWs are then computed and discussed. This chapter approaches the problem from a geometric point of view, identifying the energy-momentum tensor of GWs from their effect on the background curvature. Finally, GW propagation in curved space is discussed.

Keywords:   linearized theory, TT gauge, energy-momentum tensor, propagation of gravitational waves, geodesic equation

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