13 research outputs found
Recoil velocity at 2PN order for spinning black hole binaries
We compute the flux of linear momentum carried by gravitational waves emitted
from spinning binary black holes at 2PN order for generic orbits. In particular
we provide explicit expressions of three new types of terms, namely
next-to-leading order spin-orbit terms at 1.5 PN order, spin-orbit tail terms
at 2PN order, and spin-spin terms at 2PN order. Restricting ourselves to
quasi-circular orbits, we integrate the linear momentum flux over time to
obtain the recoil velocity as function of orbital frequency. We find that in
the so-called superkick configuration the higher-order spin corrections can
increase the recoil velocity up to about a factor 3 with respect to the
leading-order PN prediction. Furthermore, we provide expressions valid for
generic orbits, and accurate at 2PN order, for the energy and angular momentum
carried by gravitational waves emitted from spinning binary black holes.
Specializing to quasi-circular orbits we compute the spin-spin terms at 2PN
order in the expression for the evolution of the orbital frequency and found
agreement with Mik\'oczi, Vas\'uth and Gergely. We also verified that in the
limit of extreme mass ratio our expressions for the energy and angular momentum
fluxes match the ones of Tagoshi, Shibata, Tanaka and Sasaki obtained in the
context of black hole perturbation theory.Comment: 28 pages (PRD format), 1 figure, reference added, version published
in PRD, except that the PRD version contains a sign error: the sign of the
RHS of Eqs.(4.26) and (4.27) is wrong; it has been corrected in this
replacemen
Hamiltonian of a spinning test-particle in curved spacetime
Using a Legendre transformation, we compute the unconstrained Hamiltonian of
a spinning test-particle in a curved spacetime at linear order in the particle
spin. The equations of motion of this unconstrained Hamiltonian coincide with
the Mathisson-Papapetrou-Pirani equations. We then use the formalism of Dirac
brackets to derive the constrained Hamiltonian and the corresponding
phase-space algebra in the Newton-Wigner spin supplementary condition (SSC),
suitably generalized to curved spacetime, and find that the phase-space algebra
(q,p,S) is canonical at linear order in the particle spin. We provide explicit
expressions for this Hamiltonian in a spherically symmetric spacetime, both in
isotropic and spherical coordinates, and in the Kerr spacetime in
Boyer-Lindquist coordinates. Furthermore, we find that our Hamiltonian, when
expanded in Post-Newtonian (PN) orders, agrees with the Arnowitt-Deser-Misner
(ADM) canonical Hamiltonian computed in PN theory in the test-particle limit.
Notably, we recover the known spin-orbit couplings through 2.5PN order and the
spin-spin couplings of type S_Kerr S (and S_Kerr^2) through 3PN order, S_Kerr
being the spin of the Kerr spacetime. Our method allows one to compute the PN
Hamiltonian at any order, in the test-particle limit and at linear order in the
particle spin. As an application we compute it at 3.5PN order.Comment: Corrected typo in the ADM Hamiltonian at 3.5 PN order (eq. 6.20
Electromagnetic self-forces and generalized Killing fields
Building upon previous results in scalar field theory, a formalism is
developed that uses generalized Killing fields to understand the behavior of
extended charges interacting with their own electromagnetic fields. New notions
of effective linear and angular momenta are identified, and their evolution
equations are derived exactly in arbitrary (but fixed) curved spacetimes. A
slightly modified form of the Detweiler-Whiting axiom that a charge's motion
should only be influenced by the so-called "regular" component of its
self-field is shown to follow very easily. It is exact in some interesting
cases, and approximate in most others. Explicit equations describing the
center-of-mass motion, spin angular momentum, and changes in mass of a small
charge are also derived in a particular limit. The chosen approximations --
although standard -- incorporate dipole and spin forces that do not appear in
the traditional Abraham-Lorentz-Dirac or Dewitt-Brehme equations. They have,
however, been previously identified in the test body limit.Comment: 20 pages, minor typos correcte
Highly relativistic spinning particle in the Schwarzschild field: Circular and other orbits
The Mathisson-Papapetrou equations in the Schwarzschild background both at
Mathisson-Pirani and Tulczyjew-Dixon supplementary condition are considered.
The region of existence of highly relativistic circular orbits of a spinning
particle in this background and dependence of the particle's orbital velocity
on its spin and radial coordinate are investigated. It is shown that in
contrast to the highly relativistic circular orbits of a spinless particle,
which exist only for , , the corresponding
orbits of a spinning particle are allowed in a wider space region, and the
dimension of this region significantly depends on the supplementary condition.
At the Mathisson-Pirani condition new numerical results which describe some
typical cases of non-circular highly relativistic orbits of a spinning particle
starting from are presented.Comment: 10 pages, 11 figure
Spinning particles in Schwarzschild-de Sitter space-time
After considering the reference case of the motion of spinning test bodies in
the equatorial plane of the Schwarzschild space-time, we generalize the results
to the case of the motion of a spinning particle in the equatorial plane of the
Schwarzschild-de Sitter space-time. Specifically, we obtain the loci of turning
points of the particle in this plane. We show that the cosmological constant
affect the particle motion when the particle distance from the black hole is of
the order of the inverse square root of the cosmological constant.Comment: 8 pages, 5 eps figures, submitted to Gen.Rel.Gra
Stability of circular orbits of spinning particles in Schwarzschild-like space-times
Circular orbits of spinning test particles and their stability in
Schwarzschild-like backgrounds are investigated. For these space-times the
equations of motion admit solutions representing circular orbits with particles
spins being constant and normal to the plane of orbits. For the de Sitter
background the orbits are always stable with particle velocity and momentum
being co-linear along them. The world-line deviation equations for particles of
the same spin-to-mass ratios are solved and the resulting deviation vectors are
used to study the stability of orbits. It is shown that the orbits are stable
against radial perturbations. The general criterion for stability against
normal perturbations is obtained. Explicit calculations are performed in the
case of the Schwarzschild space-time leading to the conclusion that the orbits
are stable.Comment: eps figures, submitted to General Relativity and Gravitatio
Mathisson-Papapetrou-Dixon equations in the Schwarzschild and Kerr backgrounds
A new representation, which does not contain the third-order derivatives of
the coordinates, of the exact Mathisson-Papapetrou-Dixon equations, describing
the motion of a spinning test particle, is obtained under the assumption of the
Mathisson-Pirani condition in a Kerr background. For this purpose the integrals
of energy and angular momentum of the spinning particle as well as a
differential relationship following from the Mathisson-Papapetrou-Dixon
equations are used. The form of these equations is adapted for their computer
integration with the aim to investigate the influence of the spin-curvature
interaction on the particle's behavior in the gravitational field without
restrictions on its velocity and spin orientation. Some numerical examples for
a Schwarzschild background are presented.Comment: 21 pages, 11 figures. arXiv admin note: substantial text overlap with
arXiv:1105.240
Spin and quadrupole contributions to the motion of astrophysical binaries
Compact objects in general relativity approximately move along geodesics of
spacetime. It is shown that the corrections to geodesic motion due to spin
(dipole), quadrupole, and higher multipoles can be modeled by an extension of
the point mass action. The quadrupole contributions are discussed in detail for
astrophysical objects like neutron stars or black holes. Implications for
binaries are analyzed for a small mass ratio situation. There quadrupole
effects can encode information about the internal structure of the compact
object, e.g., in principle they allow a distinction between black holes and
neutron stars, and also different equations of state for the latter.
Furthermore, a connection between the relativistic oscillation modes of the
object and a dynamical quadrupole evolution is established.Comment: 43 pages. Proceedings of the 524. WE-Heraeus-Seminar "Equations of
Motion in Relativistic Gravity". v2: fixed reference. v3: corrected typos in
eqs. (1), (57), (85
Center of mass, spin supplementary conditions, and the momentum of spinning particles
We discuss the problem of defining the center of mass in general relativity
and the so-called spin supplementary condition. The different spin conditions
in the literature, their physical significance, and the momentum-velocity
relation for each of them are analyzed in depth. The reason for the
non-parallelism between the velocity and the momentum, and the concept of
"hidden momentum", are dissected. It is argued that the different solutions
allowed by the different spin conditions are equally valid descriptions for the
motion of a given test body, and their equivalence is shown to dipole order in
curved spacetime. These different descriptions are compared in simple examples.Comment: 45 pages, 7 figures. Some minor improvements, typos fixed, signs in
some expressions corrected. Matches the published version. Published as part
of the book "Equations of Motion in Relativistic Gravity", D. Puetzfeld et
al. (eds.), Fundamental Theories of Physics 179, Springer, 201