Computer Science
Scientific paper
Nov 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005phdt.........5v&link_type=abstract
Ph.D dissertation, 2005. Section 0176, Part 0605 117 pages; United States -- Pennsylvania: The Pennsylvania State University; 2
Computer Science
2
Black Holes, Neutron Stars
Scientific paper
This thesis encompasses issues in both the strong and weak field regimes of general relativity. The strong field analysis is motivated by fundamental, conceptual issues while the weak field analysis is of interest to gravitational wave phenomenology.
In the strong field regime, thanks to the notions of isolated and dynamical horizons, powerful new tools have become available for studying black holes. These frameworks are developed further. Specifically, to every isolated horizon we associate a set of mass and angular momentum multipoles, and show that these characterize the horizon in a diffeomorphism-invariant fashion. They can be thought of as the source multipoles of a black hole in equilibrium and play a key role in the black hole entropy calculation in loop quantum gravity. Their definition easily carries over to dynamical horizons, where we expect them to play a significant role in both numerical and analytical studies in classical general relativity. We then consider isolated horizons in higher dimensions and set up a Hamiltonian framework for spacetimes which admit an isolated horizon inner boundary and approach the anti-de Sitter geometry at infinity. This allows us to derive the first law of black hole mechanics in a Hamiltonian setting. Furthermore, this analysis greatly clarifies some issues concerning the definition of conserved quantities in such spacetimes. Returning to four spacetime dimensions, we study some aspects of the behavior of dynamical horizons in gravitational collapse, indicating that some of the prevailing intuition needs to be amended.
In the weak field regime, where linearized general relativity applies, we study the expected gravitational radiation from freely precessing triaxial neutron stars, which are potential sources for the Advanced LIGO detector. In older work, the gravitational wave spectrum of such objects was evaluated to first order in precession angle, leading to two spectral lines. Here we calculate the contributions to second order in the wobble angle, where a single extra line emerges. We show that the second-order spectrum may well be observable in the near future for precessing neutron stars as far away as the galactic center. Observation of the full spectrum at second order allows for a direct measurement of the star's wobble angle, oblateness, and deviation from axisymmetry, with the potential to significantly increase our understanding of neutron star structure.
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