Applications of black-hole perturbation techniques
Separable, decoupled differential equations which describe gravitational, electromagnetic, and scalar perturbations of nonrotating (Schwarzschild) and rotating (Kerr) black holes have recently become available. Fortuitously, many interesting astrophysical processes near black holes can accurately be...
| Summary: | Separable, decoupled differential equations which describe gravitational, electromagnetic, and scalar perturbations of nonrotating (Schwarzschild) and rotating (Kerr) black holes have recently become available. Fortuitously, many interesting astrophysical processes near black holes can accurately be studied with these perturbation equations. A number of such processes are here investigated (as well as some matters of principle in pure relativity): "vibrations" of black holes, and the long wave-trains of gravitational waves which such vibrations may generate; the spectrum and intensity of gravitational radiation from a particle falling radially into a Schwarzschild hole; the physical significance of the Newman-Penrose conserved quantities, the result that they are never physically measurable and do not always exist; the time evolution of a rotating black hole immersed in a static scalar field, a quantitative calculation of the hole's "spin-down" and "alignment"; scalar-field calculations of superradiant wave scattering from a rotating black hole, and of the possibility of "floating orbits" — these are both wave processes which extract a hole's rotational energy. Included is a discussion of how these scalar-field results can be extended to the electromagnetic and gravitational cases. The most important perturbation problem yet to be solved is the question of whether rotating black holes are stable (against processes which would spontaneously emit gravitational waves). The astrophysical implications of instabilities are discussed, and a method for deciding the stability question (on which work is in progress) is outlined in detail. An appendix includes additional work on peripherally related matters. Several papers included in this thesis are extended from their published form by a more detailed discussion of numerical methods.
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