S Deser and Bayram Tekin 2003 Class. Quantum Grav. 20 4877 doi:10.1088/0264-9381/20/22/011
S Deser1 and Bayram Tekin1,2
Show affiliationsWe 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.
11.30.Ly Other internal and higher symmetries
04.20.Fy Canonical formalism, Lagrangians, and variational principles
83C47 Methods of quantum field theory (See also 81T20)
81Txx Quantum field theory; related classical field theories (See also 70Sxx)
Issue 22 (21 November 2003)
Received 26 June 2003
Published 6 October 2003
S Deser and Bayram Tekin 2003 Class. Quantum Grav. 20 4877
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