Late-time decay of gravitational and electromagnetic perturbations along the event horizon

Details Late-time decay of gravitational and electromagnetic perturbations along the event horizon Late-time decay of gravitational and electromagnetic perturbations along the event horizon

1999-07-27

arxiv.org/abs/gr-qc/9907085v2

Phys.Rev. D60 (1999) 124005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages, REVTeX; Accepted for publication in Physical Review D

Scientific paper

10.1103/PhysRevD.60.124005

We study analytically, via the Newman-Penrose formalism, the late-time decay of linear electromagnetic and gravitational perturbations along the event horizon (EH) of black holes. We first analyze in detail the case of a Schwarzschild black hole. Using a straightforward local analysis near the EH, we show that, generically, the ``ingoing'' ($s>0$) component of the perturbing field dies off along the EH more rapidly than its ``outgoing'' ($s<0$) counterpart. Thus, while along $r=const>2M$ lines both components of the perturbation admit the well-known $t^{-2l-3}$ decay rate, one finds that along the EH the $s<0$ component dies off in advanced-time $v$ as $v^{-2l-3}$, whereas the $s>0$ component dies off as $v^{-2l-4}$. We then describe the extension of this analysis to a Kerr black hole. We conclude that for axially symmetric modes the situation is analogous to the Schwarzschild case. However, for non-axially symmetric modes both $s>0$ and $s<0$ fields decay at the same rate (unlike in the Schwarzschild case).

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