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Relativity in Modern Physics$
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Nathalie Deruelle and Jean-Philippe Uzan

Print publication date: 2018

Print ISBN-13: 9780198786399

Published to Oxford Scholarship Online: October 2018

DOI: 10.1093/oso/9780198786399.001.0001

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Gravitational radiation

Gravitational radiation

(p.551) 14 Gravitational radiation
Relativity in Modern Physics

Nathalie Deruelle

Jean-Philippe Uzan

Oxford University Press

This chapter attempts to calculate the radiated energy of a source in the linear approximation of general relativity to infinity in the lowest order. For this, the chapter first expands the Einstein equations to quadratic order in metric perturbations. It reveals that the radiated energy is then given by the (second) quadrupole formula, which is the gravitational analog of the dipole formula in Maxwell theory. This formula is a priori valid only if the motion of the source is due to forces other than gravity. Finally, this chapter shows that, to prove this formula for the case of self-gravitating systems, the Einstein equations to quadratic order must be solved, and the radiative field in the post-linear approximation of general relativity obtained.

Keywords:   gravitational radiation, general relativity, Einstein equations, metric perturbations, radiated energy, quadrupole formula, self-gravitating systems, quadratic order

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