51 research outputs found
Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings
We demonstrate equivalences, under simple mappings, between the dynamics of
three distinct systems---(i) an arbitrary-mass-ratio two-spinning-black-hole
system, (ii) a spinning test black hole in a background Kerr spacetime, and
(iii) geodesic motion in Kerr---when each is considered in the first
post-Minkowskian (1PM) approximation to general relativity, i.e. to linear
order but to all orders in , and to all orders in the black holes'
spins, with all orders in the multipole expansions of their linearized
gravitational fields. This is accomplished via computations of the net results
of weak gravitational scattering encounters between two spinning black holes,
namely the net changes in the holes' momenta and spins as functions of
the incoming state. The results are given in remarkably simple closed forms,
found by solving effective Mathisson-Papapetrou-Dixon-type equations of motion
for a spinning black hole in conjunction with the linearized Einstein equation,
with appropriate matching to the Kerr solution. The scattering results fully
encode the gauge-invariant content of a canonical Hamiltonian governing
binary-black-hole dynamics at 1PM order, for generic (unbound and bound) orbits
and spin orientations. We deduce one such Hamiltonian, which reproduces and
resums the 1PM parts of all such previous post-Newtonian results, and which
directly manifests the equivalences with the test-body limits via simple
effective-one-body mappings.Comment: 26 pages, 2 figures. v2: added references; corrected typos in
Appendix A; added missing link in Eq. (B11
Properties of an affine transport equation and its holonomy
An affine transport equation was used recently to study properties of angular
momentum and gravitational-wave memory effects in general relativity. In this
paper, we investigate local properties of this transport equation in greater
detail. Associated with this transport equation is a map between the tangent
spaces at two points on a curve. This map consists of a homogeneous (linear)
part given by the parallel transport map along the curve plus an inhomogeneous
part, which is related to the development of a curve in a manifold into an
affine tangent space. For closed curves, the affine transport equation defines
a "generalized holonomy" that takes the form of an affine map on the tangent
space. We explore the local properties of this generalized holonomy by using
covariant bitensor methods to compute the generalized holonomy around geodesic
polygon loops. We focus on triangles and "parallelogramoids" with sides formed
from geodesic segments. For small loops, we recover the well-known result for
the leading-order linear holonomy ( Riemann area), and we derive
the leading-order inhomogeneous part of the generalized holonomy (
Riemann area). Our bitensor methods let us naturally compute
higher-order corrections to these leading results. These corrections reveal the
form of the finite-size effects that enter into the holonomy for larger loops;
they could also provide quantitative errors on the leading-order results for
finite loops.Comment: 18 pages, 4 figures, new short section (Sec. 5) in v3; updated to
match article published in GR
Scattering of Spinning Black Holes from Exponentiated Soft Factors
We provide evidence that the classical scattering of two spinning black holes
is controlled by the soft expansion of exchanged gravitons. We show how an
exponentiation of Cachazo-Strominger soft factors, acting on massive
higher-spin amplitudes, can be used to find spin contributions to the
aligned-spin scattering angle, conjecturally extending previously known results
to higher orders in spin at one-loop order. The extraction of the classical
limit is accomplished via the on-shell leading-singularity method and using
massive spinor-helicity variables. The three-point amplitude for arbitrary-spin
massive particles minimally coupled to gravity is expressed in an exponential
form, and in the infinite-spin limit it matches the effective stress-energy
tensor of the linearized Kerr solution. A four-point gravitational Compton
amplitude is obtained from an extrapolated soft theorem, equivalent to gluing
two exponential three-point amplitudes, and becomes itself an exponential
operator. The construction uses these amplitudes to: 1) recover the known
tree-level scattering angle at all orders in spin, 2) recover the known
one-loop linear-in-spin interaction, 3) match a previous conjectural expression
for the one-loop scattering angle at quadratic order in spin, 4) propose new
one-loop results through quartic order in spin. These connections link the
computation of higher-multipole interactions to the study of deeper orders in
the soft expansion.Comment: 29 pages + appendices + refs, 3 figures; v3 minor corrections,
journal versio
Hyperbolic scattering of spinning particles by a Kerr black hole
We investigate the scattering of a spinning test particle by a Kerr black
hole within the Mathisson-Papapetrou-Dixon model to linear order in spin. The
particle's spin and orbital angular momentum are taken to be aligned with the
black hole's spin. Both the particle's mass and spin length are assumed to be
small in comparison with the characteristic length scale of the background
curvature, in order to avoid backreaction effects. We analytically compute the
modifications due to the particle's spin to the scattering angle, the
periastron shift, and the condition for capture by the black hole, extending
previous results valid for the nonrotating Schwarzschild background. Finally,
we discuss how to generalize the present analysis beyond the linear
approximation in spin, including spin-squared corrections in the case of a
black-hole-like quadrupolar structure for the extended test body.Comment: 12 pages, 3 figures, revtex macro
Gravitational waves from spinning binary black holes at the leading post-Newtonian orders at all orders in spin
We determine the binding energy, the total gravitational wave energy flux,
and the gravitational wave modes for a binary of rapidly spinning black holes,
working in linearized gravity and at leading orders in the orbital velocity,
but to all orders in the black holes' spins. Though the spins are treated
nonperturbatively, surprisingly, the binding energy and the flux are given by
simple analytical expressions which are finite (respectively third- and
fifth-order) polynomials in the spins. Our final results are restricted to the
important case of quasi-circular orbits with the black holes' spins aligned
with the orbital angular momentum.Comment: 16 pages, 1 figure; updated to match published versio
Canonical Hamiltonian for an extended test body in curved spacetime: To quadratic order in spin
We derive a Hamiltonian for an extended spinning test body in a curved
background spacetime, to quadratic order in the spin, in terms of
three-dimensional position, momentum, and spin variables having canonical
Poisson brackets. This requires a careful analysis of how changes of the spin
supplementary condition are related to shifts of the body's representative
worldline and transformations of the body's multipole moments, and we employ
bitensor calculus for a precise framing of this analysis. We apply the result
to the case of the Kerr spacetime and thereby compute an explicit canonical
Hamiltonian for the test-body limit of the spinning two-body problem in general
relativity, valid for generic orbits and spin orientations, to quadratic order
in the test spin. This fully relativistic Hamiltonian is then expanded in
post-Newtonian orders and in powers of the Kerr spin parameter, allowing
comparisons with the test-mass limits of available post-Newtonian results. Both
the fully relativistic Hamiltonian and the results of its expansion can inform
the construction of waveform models, especially effective-one-body models, for
the analysis of gravitational waves from compact binaries.Comment: RevTeX, 25 pages, 2 figures. v2: Updated to match PRD version;
further references added; some changes in presentation and notation;
typographical errors corrected, most notably in Eqs. (7.51) and (7.58
Hairy binary black holes in Einstein-Maxwell-dilaton theory and their effective-one-body description
In General Relativity and many modified theories of gravity, isolated black
holes (BHs) cannot source massless scalar fields. Einstein-Maxwell-dilaton
(EMd) theory is an exception: through couplings both to electromagnetism and
(non-minimally) to gravity, a massless scalar field can be generated by an
electrically charged BH. In this work, we analytically model the dynamics of
binaries comprised of such scalar-charged ("hairy") BHs. While BHs are not
expected to have substantial electric charge within the Standard Model of
particle physics, nearly-extremally charged BHs could occur in models of
minicharged dark matter and dark photons. We begin by studying the test-body
limit for a binary BH in EMd theory, and we argue that only very compact
binaries of nearly-extremally charged BHs can manifest non-perturbative
phenomena similar to those found in certain scalar-tensor theories. Then, we
use the post-Newtonian approximation to study the dynamics of binary BHs with
arbitrary mass ratios. We derive the equations governing the conservative and
dissipative sectors of the dynamics at next-to-leading order, use our results
to compute the Fourier-domain gravitational waveform in the stationary-phase
approximation, and compute the number of useful cycles measurable by the
Advanced LIGO detector. Finally, we construct two effective-one-body (EOB)
Hamiltonians for binary BHs in EMd theory: one that reproduces the exact
test-body limit and another whose construction more closely resembles similar
models in General Relativity, and thus could be more easily integrated into
existing EOB waveform models used in the data analysis of gravitational-wave
events by the LIGO and Virgo collaborations.Comment: 36 pages, 12 figures, updated to match published versio
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