Topics in general relativity : naked singularities, and theoretical aspects of gravitational waves from merging compact binaries

Citation

Apostolatos, Theocaris A. (1995) Topics in general relativity : naked singularities, and theoretical aspects of gravitational waves from merging compact binaries. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2x5m-b994. https://resolver.caltech.edu/CaltechETD:etd-09112007-132644

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Two topics in classical general relativity are discussed: a) The clothing of singularities by event horizons, and b) various issues in the evolution of coalescing compact binaries, as sources of gravitational waves to be detected by the LIGO/VIRGO/GEO ground-based detectors and/or the LISA space-based detector. More specifically: We investigate a problem related to an important conjecture of classical relativity, namely the existence of a "cosmic censorship" that forbids the formation of naked singularities, and always clothes them with event horizons that causally hide them from the rest of the Universe. Under consideration is the role of rotation in an infinite cylindrical shell consisting of collisionless dust particles, half of which rotate clockwise and half counterclockwise. We show that, although such a shell without any rotation is known to collapse into a line singularity, the presence of an arbitrarily small amount of rotation is sufficient to halt the collapse. Such a shell, starting from a non equibrium configuration, will "breath" radially, emitting gravitational waves, and will finally settle down to an equilibrium radius at which gravity is balanced by centrifugal forces. This suggests the essential role that rotation might play in halting the gravitational collapse of an elongated distribution of mass and preventing the formation of a naked singularity. However, this is a highly idealized example, and it can, by no means, ensure the validity of the "cosmic censorship" hypothesis. On a separate topic, we explore the details of how gravitational radiation reaction drives the evolution of a slightly eccentric orbit of a small body around nonrotating supermassive black holes. A combination of analytic and numerical results arise from the solution of the Teukolsky perturbation equation. It is shown that in the fully relativistic situation, as in the Newtonian quadrupole approximation, there is a tendency for circularization of the orbit down to an orbital radius [...], where M is the mass of the black hole, and G and c are Newton's gravitation constant and the speed of light. It is further shown that for radii smaller than [...] the eccentricity increases. Finally, an attempt is made to understand and construct analytic expressions that, based on the laws of general relativity, approximately describe the simultaneous precession in rapidly spinning black hole and/or neutron star and inspiral binaries with circular orbits. The precession is produced by general relativistic spin-orbit and spin-spin coupling; the inspiral, by gravitational radiation reaction. We derive the corresponding approximate waveforms to be received by the network of LIGO, VIRGO, and GEO earth-based gravitational-wave detectors. We then go on to investigate the adequateness of various "families of templates," to detect these spin-modulated waveforms by the method of "matching filters," We introduce a "fitting factor" FF as a measure of templates' adequateness, and show the complete inadequateness, for the task of detection, of the "Newtonian template family" (the set of the waveforms derived from the Newtonian, quadrupole approximation formalism). Another template family with an extra parameter is suggested that performs much better.

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