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Shortcuts to high symmetry solutions in gravitational theories

Deser, S. and Tekin, Bayram (2003) Shortcuts to high symmetry solutions in gravitational theories. Classical and Quantum Gravity, 20 (22). pp. 4877-4883. ISSN 0264-9381. doi:10.1088/0264-9381/20/22/011.

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We apply the Weyl method, as sanctioned by Palais' symmetric criticality theorems, to obtain those—highly symmetric—geometries amenable to explicit solution, in generic gravitational models and dimension. The technique consists of judiciously violating the rules of variational principles by inserting highly symmetric, and seemingly gauge fixed, metrics into the action, then varying it directly to arrive at a small number of transparent, indexless, field equations. Illustrations include spherically and axially symmetric solutions in a wide range of models beyond D = 4 Einstein theory; already at D = 4, novel results emerge such as exclusion of Schwarzschild solutions in cubic curvature models and restrictions on 'independent' integration parameters in quadratic ones. Another application of Weyl's method is an easy derivation of Birkhoff's theorem in systems with only tensor modes. Other uses are also suggested.

Item Type:Article
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URLURL TypeDescription Paper
Deser, S.0000-0001-9285-9434
Additional Information:© 2003 IOP Publishing Ltd. Received 26 June 2003; Published 6 October 2003. We thank R S Palais for patient discussions of his work and N Wyllard for algebraic assistance. This research was supported by NSF grant 99-73935.
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Issue or Number:22
Classification Code:PACS numbers: 04.20.−q, 04.20.Jb, 04.20.Fy
Record Number:CaltechAUTHORS:20170524-131659063
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Official Citation:S Deser and Bayram Tekin 2003 Class. Quantum Grav. 20 4877
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77717
Deposited By: Tony Diaz
Deposited On:24 May 2017 21:16
Last Modified:12 Jul 2022 19:51

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