Second- and higher-order perturbations of a spherical spacetime
- 30 August 2006
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 74 (4), 044039
- https://doi.org/10.1103/physrevd.74.044039
Abstract
The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory. The GS harmonics are generalized to an arbitrary number of indices on the unit sphere and a formula is given for their products. The formalism is optimized for its implementation in a computer-algebra system, something that becomes essential in practice given the size and complexity of the equations. All evolution equations for the second-order perturbations, as well as the conservation equations for the energy-momentum tensor at this perturbation order, are given in covariant form, in Regge-Wheeler gauge.Keywords
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