Citation
Hartl, Michael David (2003) Dynamics of spinning compact binaries in general relativity. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KZ5MMR27. https://resolver.caltech.edu/CaltechETD:etd05222003161626
Abstract
This thesis investigates the dynamics of binary systems composed of spinning compact objects (such as white dwarfs, neutron stars, and black holes) in the context of general relativity. In particular, we use the method of Lyapunov exponents to determine whether such systems are chaotic. Compact binaries are promising sources of gravitational radiation for both ground and spacebased gravitationalwave detectors, and radiation from chaotic orbits would be difficult to detect and analyze. For chaotic orbits, the number of waveform templates needed to match a given gravitationalwave signal would grow exponentially with increasing detection sensitivity, rendering the preferred matched filter detection method computationally impractical. It is therefore urgent to understand whether the binary dynamics can be chaotic, and, if so, how prevalent this chaos is. We first consider the dynamics of a spinning compact object orbiting a much more massive rotating black hole, as modeled by the Papapetrou equations in Kerr spacetime. We find that many initial conditions lead to positive Lyapunov exponents, indicating chaotic dynamics. The Lyapunov exponents come in positive/negative pairs, a characteristic of Hamiltonian dynamical systems. Despite the formal existence of chaotic solutions, we find that chaos occurs only for physically unrealistic values of the small body's spin. As a result, chaos will not affect theoretical templates in the extreme massratio limit for which the Papapetrou equations are valid. Chaos will therefore not affect the ability of spacebased gravitationalwave detectors (such as LISA, the Laser Interferometer Space Antenna) to perform precision tests of general relativity using extreme massratio inspirals. We next consider the dynamics of spinning blackhole binaries, as modeled by the postNewtonian (PN) equations, which are valid for orbital velocities much smaller than the speed of light. We study thoroughly the special case of quasicircular orbits with comparable mass ratios, which are particularly relevant from the perspective of gravitational wave generation for LIGO (the Laser Interferometer Gravitationalwave Observatory) and other groundbased interferometers. In this case, unlike the extreme massratio case, we find chaotic solutions for physically realistic values of the spin. On the other hand, our survey shows that chaos occurs in a negligible fraction of possible configurations, and only for such small radii that the PN approximation is likely to be invalid. As a result, at least in the case of comparable mass blackhole binaries, theoretical templates will not be significantly affected by chaos. In a final, selfcontained chapter, we discuss various methods for the calculation of Lyapunov exponents in systems of ordinary differential equations. We introduce several new techniques applicable to constrained dynamical systems, developed in the course of studying the dynamics of spinning compact binaries. Considering the Papapetrou and postNewtonian systems together, our most important general conclusion is that we find no chaos in any relativistic binary system for orbits that clearly satisfy the approximations required for the equations of motion to be physically valid.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  chaos theory; compact binaries; gravitational waves; Lyapunov exponents 
Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Group:  TAPIR, Astronomy Department 
Thesis Committee: 

Defense Date:  22 May 2003 
Record Number:  CaltechETD:etd05222003161626 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd05222003161626 
DOI:  10.7907/KZ5MMR27 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1940 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  23 May 2003 
Last Modified:  10 Mar 2020 23:05 
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