Second and higher-order perturbations of a spherical spacetime

Details Second and higher-order perturbations of a spherical spacetime Second and higher-order perturbations of a spherical spacetime

2006-07-06

arxiv.org/abs/gr-qc/0607025v1

Phys.Rev. D74 (2006) 044039

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Accepted for publication in Physical Review D

Scientific paper

10.1103/PhysRevD.74.044039

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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