2003/06/26 by S. Deser, Bayram Tekin · 11 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/20/22/011
published as Class.Quant.Grav.20:4877-4884,2003 · 10 pages
arxiv created 2003/06/26 · openalex publication_date 2003/10/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.