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Second and higher-order perturbations of a spherical spacetime

David Brizuela·Jose M. Martin-Garcia·Guillermo A. Mena Marugan
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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.

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David Brizuela, Jose M. Martin-Garcia, Guillermo A. Mena Marugan. 2006-07-06. Second and higher-order perturbations of a spherical spacetime. https://doi.org/10.1103/physrevd.74.044039

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