Computer Science
Scientific paper
Jan 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994phdt........15f&link_type=abstract
Thesis (PH.D.)--CALIFORNIA INSTITUTE OF TECHNOLOGY, 1994.Source: Dissertation Abstracts International, Volume: 55-05, Section: B
Computer Science
Scientific paper
The hoop conjecture states that an event horizon will form around a collapsing body of mass M when and only when the body becomes smaller than ~GM/ c^2 in all three spatial dimensions. We show in that some static, axisymmetric solutions to Einstein's equations are consistent with this conjecture. We show that for momentarily static, conformally flat, axisymmetric solutions of the initial-value equations, whenever the minimum value of the circumferences (or of the square roots of the areas) of all surfaces surrounding the source region is greater than a constant times the "ADM mass," then none of the level surfaces of the conformal factor can be "outer trapped.". The second half of the thesis deals with theoretical aspects of the effort to detect gravitational waves from cosmic sources. We identify the optimal data analysis method for searching for a stochastic background of gravitational waves with a network of laser-interferometer gravitational -wave detectors, and analyze the network's sensitivity to the background radiation, and determine how this sensitivity depends on the detectors orientations. We show that the minimum detectable stochastic energy-density for the LIGO pair of detectors, with their planned orientations, is ~3% greater than what it would be if the orientations were optimal, and is ~ 4 times what it would be if their separation were _sp{~}< a few kilometers instead of the actual distance of ~3000 km. In the frequency range 20 Hz _sp{~}< f _sp{~}< 70 Hz, the sensitivity level of the LIGO detector pair at an advanced stage of development will be roughly Omega_{rm gw}~ 5 times 10^{-10}.. Lastly, we explore the information that can be extracted, by LIGO and its European companion VIRGO, from the gravitational waves emitted by inspiralling neutron -star/neutron-star binaries, neutron-star/black-hole binaries, and black-hole/black-hole binaries. We show, for example, that: (i) a particular combination of the binaries' two masses will be measurable to within ~0.1% -1%, (ii) the individual masses will be measurable to within ~10%, and (iii) the distance to the source will typically be measurable to within ~30%.
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