From Measure Zero to Measure Hero: Periodic Kerr Orbits and Gravitational Wave Physics

Title:

From Measure Zero to Measure Hero: Periodic Kerr Orbits and Gravitational Wave Physics

Author(s):

PerezGiz, Gabe

Thesis Advisor(s):

Hui, Lam

Date:

2011

Type:

Dissertations

Department:

Physics

Permanent URL:

http://hdl.handle.net/10022/AC:P:11008

Notes:

Ph.D., Columbia University.

Abstract:

A direct observational detection of gravitational waves  perhaps the most fundamental prediction of a theory of curved spacetime  looms close at hand. Stellar mass compact objects spiraling into supermassive black holes have received particular attention as sources of gravitational waves detectable by spacebased gravitational wave observatories. A wellestablished approach models such an extreme mass ratio inspirals (EMRI) as an adiabatic progression through a series of Kerr geodesics. Thus, the direct detection of gravitational radiation from EMRIs and the extraction of astrophysical information from those waveforms require a thorough knowledge of the underlying geodesic dynamics. This dissertation adopts a dynamical systems approach to the study of Kerr orbits, beginning with equatorial orbits. We deduce a topological taxonomy of orbits that hinges on a correspondence between periodic orbits and rational numbers. The taxonomy defines the entire dynamics, including aperiodic motion, since every orbit is in or near the periodic set. A remarkable implication of this periodic orbit taxonomy is that the simple precessing ellipse familiar from planetary orbits is not allowed in the strongfield regime. Instead, eccentric orbits trace out precessions of multileaf clovers in the final stages of inspiral. Furthermore, for any black hole, there is some orbital angular momentum value in the strongfield regime below which zoomwhirl behavior becomes unavoidable. We then generalize the taxonomy to help identify nonequatorial orbits whose radial and polar frequencies are rationally related, or in resonance. The thesis culminates by describing how those resonant orbits can be leveraged for an order of magnitude or more reduction in the computational cost of adiabatic order EMRI trajectories, which are so prohibitively expensive that no such relativistically correct inspirals have been generated to date.

Subject(s):

Physics
Astrophysics
Applied mathematics
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