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

Abstract

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).

arXiv comment30 pages, REVTeX; Accepted for publication in Physical Review D

References in corpus (17)

• Late-Time Behavior of Stellar Collapse and Explosions: I. Linearized Perturbations
• Late-Time Behavior of Stellar Collapse and Explosions: II. Nonlinear Evolution
• Evolving test-fields in a black-hole geometry
• Black hole singularities: a numerical approach
• Late Time Tail of Wave Propagation on Curved Spacetime
• Dynamics of perturbations of rotating black holes
• Telling Tails In The Presence Of A Cosmological Constant
• Late-time evolution of nonlinear gravitational collapse
• Late-time decay of scalar perturbations outside rotating black holes
• Dynamics of Scalar Fields in the Background of Rotating Black Holes
• Late-Time Tails in Gravitational Collapse of a Self-Interacting (Massive) Scalar-Field and Decay of a Self-Interacting Scalar Hair
• Late-Time Evolution of Charged Gravitational Collapse and Decay of Charged Scalar Hair - III. Nonlinear Analysis
• Late time dynamics of scalar perturbations outside black holes: II. Schwarzschild geometry
• Late-Time Evolution of Realistic Rotating Collapse and The No-Hair Theorem
• Late time decay of scalar, electromagnetic, and gravitational perturbations outside rotating black holes
• The late-time singularity inside non-spherical black holes
• Late time dynamics of scalar perturbations outside black holes: I. A shell toy-model

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