Gravitational radiation in D-dimensional space-times

Gravitational radiation in D-dimensional space-times

Gravitational wave solutions to Einstein’s equations and their generation are examined in D-dimensional flat spacetimes. First the plane wave solutions are analyzed; then the wave generation is studied with the solution for the metric tensor being obtained with the help of retarded D-dimensional Green’s functions. Because of the difficulties in handling the wave tails in odd dimensions we concentrate our study on even dimensions. We compute the metric quantities in the wave zone in terms of the energy-momentum tensor at retarded time. Some special cases of interest are studied. First we study the slow motion approximation, where the D-dimensional quadrupole formula is deduced. Within the quadrupole approximation, we consider two cases of interest: a particle in circular orbit and a particle falling radially into a higher dimensional Schwarzschild black hole. Then we turn our attention to the gravitational radiation emitted during collisions lasting zero seconds, i.e., hard collisions. We compute the gravitational energy radiated during the collision of two point particles, in terms of a cutoff frequency. In the case in which at least one of the particles is a black hole, we argue that this cutoff frequency should be close to the lowest gravitational quasinormal frequency. In this context, we compute the scalar quasinormal frequencies of higher dimensional Schwarzschild black holes. Finally, as an interesting new application of this formalism, we compute the gravitational energy release during the quantum process of black hole pair creation. These results might be important in light of the recent proposal that there may exist extra dimensions in the Universe, one consequence of which may be black hole creation at the Large Hadron Collider at CERN.

Cardoso, Vitor

08c1bdef-b56a-4067-ab37-89a9ece74fb7

Dias, Oscar J.C.

f01a8d9b-9597-4c32-9226-53a6e5500a54

Lemos, Jose P.S.

4e94199c-42b9-4592-9da9-f5035913088c

15 March 2003

Cardoso, Vitor

08c1bdef-b56a-4067-ab37-89a9ece74fb7

Dias, Oscar J.C.

f01a8d9b-9597-4c32-9226-53a6e5500a54

Lemos, Jose P.S.

4e94199c-42b9-4592-9da9-f5035913088c

Cardoso, Vitor, Dias, Oscar J.C. and Lemos, Jose P.S.
(2003)
Gravitational radiation in D-dimensional space-times.
*Phys.Rev.D*, 67 (6).
(doi:10.1103/PhysRevD.67.064026).

## Abstract

Gravitational wave solutions to Einstein’s equations and their generation are examined in D-dimensional flat spacetimes. First the plane wave solutions are analyzed; then the wave generation is studied with the solution for the metric tensor being obtained with the help of retarded D-dimensional Green’s functions. Because of the difficulties in handling the wave tails in odd dimensions we concentrate our study on even dimensions. We compute the metric quantities in the wave zone in terms of the energy-momentum tensor at retarded time. Some special cases of interest are studied. First we study the slow motion approximation, where the D-dimensional quadrupole formula is deduced. Within the quadrupole approximation, we consider two cases of interest: a particle in circular orbit and a particle falling radially into a higher dimensional Schwarzschild black hole. Then we turn our attention to the gravitational radiation emitted during collisions lasting zero seconds, i.e., hard collisions. We compute the gravitational energy radiated during the collision of two point particles, in terms of a cutoff frequency. In the case in which at least one of the particles is a black hole, we argue that this cutoff frequency should be close to the lowest gravitational quasinormal frequency. In this context, we compute the scalar quasinormal frequencies of higher dimensional Schwarzschild black holes. Finally, as an interesting new application of this formalism, we compute the gravitational energy release during the quantum process of black hole pair creation. These results might be important in light of the recent proposal that there may exist extra dimensions in the Universe, one consequence of which may be black hole creation at the Large Hadron Collider at CERN.

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## More information

Published date: 15 March 2003

Additional Information:
©2003 American Physical Society

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Local EPrints ID: 467707

URI: http://eprints.soton.ac.uk/id/eprint/467707

PURE UUID: b9893619-966f-4696-933d-8dcf5a7b9d63

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Date deposited: 19 Jul 2022 16:57

Last modified: 20 Jul 2022 01:48

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## Contributors

Author:
Vitor Cardoso

Author:
Jose P.S. Lemos

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