Topics in Gravitational Physics: Tidal Coupling in Gravitational Wave Searches and Mach’s Principle

Author: Fang, Hua

Year: 2007

Degree: Dissertation (Ph.D.)

Advisor: Thorne, Kip S.

Committee Members: Thorne, Kip S.; Cutler, Curt J.; Phinney, E. Sterl; Libbrecht, Kenneth George

Option: Physics; Electrical Engineering

DOI: 10.7907/D99H-J577

Abstract

The gravitational waves emitted by a compact object inspirling into a massive central body (e.g., a massive black hole) contain exquisite information about the spacetime geometry around that body and the tidal interaction (energy and angular momentum transfer) between the body and the inspiraling object's orbit. The first part (chapter 2--4) of this thesis studies several topics in the frame work of gravitation-wave search. In chapter 2 (in collaboration with G. Lovelace), we study the tidal interaction between a non-rotating black hole and circularly orbiting moon. Our analysis shows that the static induced quadrupole moment of the black hole is inherently ambiguous. In chapter 3, we give a survey of initial explorations of the prospects for using Advanced LIGO to detect gravitational waves from intermediate-mass-ratio inspirals (IMRIs))---analogous to the extreme-mass-ratio inspirals (EMRIs) targeted by LISA. We describe initial estimates of the detection range and the number of IMRI wave cycles in the Advanced LIGO band. We also give a detailed analysis of Advanced LIGO's accuracy for measuring the tide-induced energy transfer between the central black hole and the orbit. In chapter 4 (in collaboration with S. Babak, J. R. Gair, K. Glampedakis, and S. Hughes), we describe a new waveform-generating scheme in the context of LISA's data analysis for EMRI waves. The result is a family of "Numerical Kludge" waveforms, which share remarkable agreement with the more rigorous, but more computational-intensive Teukolsky-based waveforms.

The second part (chapter 5) of this thesis (in collaboration with K. S. Thorne) discusses another prediction from general relativity, the dragging of inertial frames, in connection with Mach's principle. We idealize our universe as a homogeneous, isotropic expanding, and slowly rotating sphere, surrounded by vacuum. We find that as the universe expands, the frame dragging weakens at its center; and that at later times inertia at the center completely breaks free of the grip of the universe's rotating matter.

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