61 research outputs found
Comment on "Ruling out chaos in compact binary systems"
In a recent Letter, Schnittman and Rasio argue that they have ruled out chaos
in compact binary systems since they find no positive Lyapunov exponents. In
stark constrast, we find that the chaos discovered in the original paper under
discussion, J.Levin, PRL, 84 3515 (2000), is confirmed by the presence of
positive Lyapunov exponents.Comment: 1 page. Published Versio
Big Black Hole, Little Neutron Star: Magnetic Dipole Fields in the Rindler Spacetime
As a black hole and neutron star approach during inspiral, the field lines of
a magnetized neutron star eventually thread the black hole event horizon and a
short-lived electromagnetic circuit is established. The black hole acts as a
battery that provides power to the circuit, thereby lighting up the pair just
before merger. Although originally suggested as a promising electromagnetic
counterpart to gravitational-wave detection, the luminous signals are promising
more generally as potentially detectable phenomena, such as short gamma-ray
bursts. To aid in the theoretical understanding, we present analytic solutions
for the electromagnetic fields of a magnetic dipole in the presence of an event
horizon. In the limit that the neutron star is very close to a Schwarzschild
horizon, the Rindler limit, we can solve Maxwell's equations exactly for a
magnetic dipole on an arbitrary worldline. We present these solutions here and
investigate a proxy for a small segment of the neutron star orbit around a big
black hole. We find that the voltage the black hole battery can provide is in
the range ~10^16 statvolts with a projected luminosity of 10^42 ergs/s for an
M=10M_sun black hole, a neutron star with a B-field of 10^12 G, and an orbital
velocity ~0.5c at a distance of 3M from the horizon. Larger black holes provide
less power for binary separations at a fixed number of gravitational radii. The
black hole/neutron star system therefore has a significant power supply to
light up various elements in the circuit possibly powering jets, beamed
radiation, or even a hot spot on the neutron star crust.Comment: Published in Physical Review D:
http://link.aps.org/doi/10.1103/PhysRevD.88.06405
Dynamics of Black Hole Pairs II: Spherical Orbits and the Homoclinic Limit of Zoom-Whirliness
Spinning black hole pairs exhibit a range of complicated dynamical behaviors.
An interest in eccentric and zoom-whirl orbits has ironically inspired the
focus of this paper: the constant radius orbits. When black hole spins are
misaligned, the constant radius orbits are not circles but rather lie on the
surface of a sphere and have acquired the name "spherical orbits". The
spherical orbits are significant as they energetically frame the distribution
of all orbits. In addition, each unstable spherical orbit is asymptotically
approached by an orbit that whirls an infinite number of times, known as a
homoclinic orbit. A homoclinic trajectory is an infinite whirl limit of the
zoom-whirl spectrum and has a further significance as the separatrix between
inspiral and plunge for eccentric orbits. We work in the context of two
spinning black holes of comparable mass as described in the 3PN Hamiltonian
with spin-orbit coupling included. As such, the results could provide a testing
ground of the accuracy of the PN expansion. Further, the spherical orbits could
provide useful initial data for numerical relativity. Finally, we comment that
the spinning black hole pairs should give way to chaos around the homoclinic
orbit when spin-spin coupling is incorporated.Comment: 16 pages, several figure
Brane-World Motion in Compact Dimensions
The topology of extra dimensions can break global Lorentz invariance,singling
out a globally preferred frame even in flat spacetime. Through experiments that
probe global topology, an observer can determine her state of motion with
respect to the preferred frame. This scenario is realized if we live on a brane
universe moving through a flat space with compact extra dimensions. We identify
three experimental effects due to the motion of our universe that one could
potentially detect using gravitational probes. One of these relates to the
peculiar properties of the twin paradox in multiply-connected spacetimes.
Another relies on the fact that the Kaluza-Klein modes of any bulk field are
sensitive to boundary conditions. A third concerns the modification to the
Newtonian potential on a moving brane. Remarkably, we find that even small
extra dimensions are detectable by brane observers if the brane is moving
sufficiently fast
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