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Topics in General Relativity: Binary Black Holes and Hyperbolic Formulations of Einstein's Equations


Alvi, Kashif Siddiq (2002) Topics in General Relativity: Binary Black Holes and Hyperbolic Formulations of Einstein's Equations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5S0S-MF65.


This thesis consists of three projects in general relativity on topics related to binary black holes and the gravitational waves they emit. The first project involves calculating a four-metric that is an approximate solution to Einstein's equations representing two widely separated nonrotating black holes in a circular orbit. This metric is constructed by matching a post-Newtonian metric to two tidally distorted Schwarzschild metrics using the framework of matched asymptotic expansions. The four-metric presented here provides physically realistic initial data that are tied to the binary's inspiral phase and can be evolved numerically to determine the gravitational wave output during the late stages of inspiral as well as the merger.

The second project is on the tidal interaction of binary black holes during the inspiral phase. The holes' tidal distortion results in the flow of energy and angular momentum into or out of the holes in a process analogous to Newtonian tidal friction in a planet-moon system. The changes in the black holes' masses, spins, and horizon areas during inspiral are calculated for a circular binary with holes of possibly comparable masses. The absorption or emission of energy and angular momentum by the holes is shown to have a negligible influence on the binary 's orbital evolution when the holes have comparable masses. The tidal-interaction analysis presented in this thesis is applicable to a black hole in a binary with any companion body (e.g., a neutron star) that is well separated from the hole.

The final project is on first-order hyperbolic formulations of Einstein's equations, which are promising as a basis for numerical simulation of binary black holes. This thesis presents two first-order symmetrizable hyperbolic systems that include the lapse and shift as dynamical fields and have only physical characteristic speeds. The first system may be useful in numerical work; the second system allows one to show that any solution to Einstein's equations in any gauge can be obtained using hyperbolic evolution of the entire metric, including the gauge fields.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Thorne, Kip S.
Group:TAPIR, Astronomy Department
Thesis Committee:
  • Thorne, Kip S. (chair)
  • Kamionkowski, Marc P.
  • Lindblom, Lee A.
  • Mabuchi, Hideo
Defense Date:21 May 2002
Record Number:CaltechTHESIS:01202012-112836824
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6771
Deposited By: Benjamin Perez
Deposited On:23 Jan 2012 15:36
Last Modified:05 Nov 2021 20:18

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