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Regge-Wheeler equation, linear stability, and greybody factors for dirty black holes

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arxiv 1305.1416 v4 pith:Q63OFP3I submitted 2013-05-07 gr-qc hep-thmath-phmath.MP

Regge-Wheeler equation, linear stability, and greybody factors for dirty black holes

Petarpa Boonserm (Chulalongkorn University) , Tritos Ngampitipan (Chulalongkorn University) , Matt Visser (Victoria University of Wellington) This is my paper
classification gr-qc hep-thmath-phmath.MP
keywords blackdirtyequationfactorsgreybodyholesregge-wheelerspin
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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So-called "dirty" black holes are those surrounded by non-zero stress-energy, rather than vacuum. The presence of the non-zero stress-energy modifies key features of the black hole, such as the surface gravity, Regge-Wheeler equation, linear stability, and greybody factors in a rather nontrivial way. Working within the inverse-Cowling approximation, (effectively the test-field limit), we shall present general forms for the Regge-Wheeler equation for linearized spin 0, spin 1, and axial spin 2 perturbations on an arbitrary static spherically symmetric background spacetime. Using very general features of the background spacetime, (in particular the classical energy conditions for the stress-energy surrounding the black hole), we extract several interesting and robust bounds on the behaviour of such systems, including rigorous bounds on the greybody factors for dirty black holes.

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