3,412 research outputs found
Celestial mechanics in Kerr spacetime
The dynamical parameters conventionally used to specify the orbit of a test
particle in Kerr spacetime are the energy , the axial component of the
angular momentum, , and Carter's constant . These parameters are
obtained by solving the Hamilton-Jacobi equation for the dynamical problem of
geodesic motion. Employing the action-angle variable formalism, on the other
hand, yields a different set of constants of motion, namely, the fundamental
frequencies , and associated with
the radial, polar and azimuthal components of orbital motion. These
frequencies, naturally, determine the time scales of orbital motion and,
furthermore, the instantaneous gravitational wave spectrum in the adiabatic
approximation. In this article, it is shown that the fundamental frequencies
are geometric invariants and explicit formulas in terms of quadratures are
derived. The numerical evaluation of these formulas in the case of a rapidly
rotating black hole illustrates the behaviour of the fundamental frequencies as
orbital parameters such as the semi-latus rectum , the eccentricity or
the inclination parameter are varied. The limiting cases of
circular, equatorial and Keplerian motion are investigated as well and it is
shown that known results are recovered from the general formulas.Comment: 25 pages (LaTeX), 5 figures, submitted to Class. Quantum Gra
Intermediate and extreme mass-ratio inspirals — astrophysics, science applications and detection using LISA
Black hole binaries with extreme (gtrsim104:1) or intermediate (~102–104:1) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed laser interferometer space antenna (LISA). These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany
A Note on Celestial Mechanics in Kerr Spacetime
The Hamilton-Jacobi equation for test particles in the Kerr geometry is
separable. Using action-angle variables, we establish several relations between
various physical quantities that characterize bound timelike geodesic orbits
around a spinning black hole, including the particle's rest mass, energy,
angular momentum, mean redshift and fundamental frequencies. These relations
are explicitly checked to hold true in the particular case of equatorial
circular orbits. An application to the gravitational wave-driven, adiabatic
inspiral of extreme-mass-ratio compact binaries is briefly discussed.Comment: 7 pages; matches version to appear in Class. Quant. Gra
Slowly Rotating Black Holes in Dynamical Chern-Simons Gravity: Deformation Quadratic in the Spin
We derive a stationary and axisymmetric black hole solution to quadratic
order in the spin angular momentum. The previously found, linear-in-spin terms
modify the odd-parity sector of the metric, while the new corrections appear in
the even-parity sector. These corrections modify the quadrupole moment, as well
as the (coordinate-dependent) location of the event horizon and the ergoregion.
Although the linear-in-spin metric is of Petrov type D, the quadratic order
terms render it of type I. The metric does not possess a second-order Killing
tensor or a Carter-like constant. The new metric does not possess closed
timelike curves or spacetime regions that violate causality outside of the
event horizon. The new, even-parity modifications to the Kerr metric decay less
rapidly at spatial infinity than the leading-order in spin, odd-parity ones,
and thus, the former are more important when considering black holes that are
rotating moderately fast. We calculate the modifications to the Hamiltonian,
binding energy and Kepler's third law. These modifications are crucial for the
construction of gravitational wave templates for black hole binaries, which
will enter at second post-Newtonian order, just like dissipative modifications
found previously.Comment: 21 pages, 2 figures; Typos correcte
The ergoregion in the Kerr spacetime: properties of the equatorial circular motion
We investigate in detail the circular motion of test particles on the
equatorial plane of the ergoregion in the Kerr spacetime. We consider all the
regions where circular motion is allowed, and we analyze the stability
properties and the energy and angular momentum of the test particles. We show
that the structure of the stability regions has definite features that make it
possible to distinguish between black holes and naked singularities. The naked
singularity case presents a very structured non-connected set of regions of
orbital stability, where the presence of counterrotating particles and zero
angular momentum particles for a specific class of naked singularities is
interpreted as due to the presence of a repulsive field generated by the
central source of gravity. In particular, we analyze the effects of the
dynamical structure of the ergoregion (the union of the orbital regions for
different attractor spins) on the behavior of accretion disks around the
central source. The properties of the circular motion turn out to be so
distinctive that they allow the introduction of a complete classification of
Kerr spacetimes, each class of which is characterized by different physical
effects that could be of especial relevance in observational Astrophysics. We
also identify some special black hole spacetimes where these effects could be
relevant.Comment: 19 pages, 9 figure multi-panels; 3 Tables. This and a slightly
modified version with the addition of new references and some new discussion.
To appear in EPJ
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