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General Relativity and Quantum Cosmology, gr-qc
Abstract:
We investigate the (conservative) dynamics of binary black holes using the
Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The
Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass
monopole/spin-induced quadrupole interaction terms. In the case of both
quasi-circular and eccentric orbits, we search for the presence of chaos (using
the method of Lyapunov exponents) for a large variety of initial conditions.
For quasi-circular orbits, we find no chaotic behavior for black holes with
total mass 10 - 40 solar masses when initially at a separation corresponding to
a Newtonian gravitational-wave frequency less than 150 Hz. Only for rather
small initial radial distances, for which spin-spin induced oscillations in the
radial separation are rather important, do we find chaotic solutions, and even
then they are rare. Moreover, these chaotic quasi-circular orbits are of
questionable astrophysical significance, since they originate from direct
parametrization of the equations of motion rather than from widely separated
binaries evolving to small separations under gravitational radiation reaction.
In the case of highly eccentric orbits, which for ground-based interferometers
are not astrophysically favored, we again find chaotic solutions, but only at
pericenters so small that higher order PN corrections, especially higher spin
PN corrections, should also be taken into account.
