8 research outputs found
A Periodic Table for Black Hole Orbits
Understanding the dynamics around rotating black holes is imperative to the
success of the future gravitational wave observatories. Although integrable in
principle, test particle orbits in the Kerr spacetime can also be elaborate,
and while they have been studied extensively, classifying their general
properties has been a challenge. This is the first in a series of papers that
adopts a dynamical systems approach to the study of Kerr orbits, beginning with
equatorial orbits. We define a 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 strong-field regime. Instead, eccentric orbits trace out
precessions of multi-leaf clovers in the final stages of inspiral. Furthermore,
for any black hole, there is some point in the strong-field regime past which
zoom-whirl behavior becomes unavoidable. Finally, we sketch the potential
application of the taxonomy to problems of astrophysical interest, in
particular its utility for computationally intensive gravitational wave
calculations.Comment: 42 pages, lots of figure
From Quasars to Extraordinary N-body Problems
We outline reasoning that led to the current theory of quasars and look at
George Contopoulos's place in the long history of the N-body problem. Following
Newton we find new exactly soluble N-body problems with multibody forces and
give a strange eternally pulsating system that in its other degrees of freedom
reaches statistical equilibrium.Comment: 13 pages, LaTeX with 1 postscript figure included. To appear in
Proceedings of New York Academy of Sciences, 13th Florida Workshop in
Nonlinear Astronomy and Physic
Gravity Waves, Chaos, and Spinning Compact Binaries
Spinning compact binaries are shown to be chaotic in the Post-Newtonian
expansion of the two body system. Chaos by definition is the extreme
sensitivity to initial conditions and a consequent inability to predict the
outcome of the evolution. As a result, the spinning pair will have
unpredictable gravitational waveforms during coalescence. This poses a
challenge to future gravity wave observatories which rely on a match between
the data and a theoretical template.Comment: Final version published in PR