Second Order Gauge Invariant Gravitational Perturbations of a Rotating Black Hole

Details Second Order Gauge Invariant Gravitational Perturbations of a Rotating Black Hole Second Order Gauge Invariant Gravitational Perturbations of a Rotating Black Hole

Dec 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998tx19.confe.484c&link_type=abstract

Abstracts of the 19th Texas Symposium on Relativistic Astrophysics and Cosmology, held in Paris, France, Dec. 14-18, 1998. Eds.:

Astronomy and Astrophysics

Astrophysics

Scientific paper

We investigate higher order gravitational perturbations in the Newman-Penrose formalism. Equations for the Weyl scalar psi_4, representing outgoing gravitational radiation, can be uncoupled into a single wave equation to any perturbative order. For second order perturbations about a Kerr black hole, we prove the existence of a first and second order coordinate and tetrad invariant waveform, psi by explicit construction. This waveform is formed by the second order piece of psi_4 plus a term, quadratic in first order perturbations, chosen to make psi totally invariant. psi fulfils a single wave equation of the form {cal T}psi = S, where {cal T} is the same wave operator as for first order perturbations and S is a source term build up out of first order perturbations. We discuss the issues of imposition of initial data to this equation, computation of the energy radiated and wave extraction for direct comparision with full numerical approachs to solve Einstein equations.

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