34 research outputs found
On the comparison of results regarding the post-Newtonian approximate treatment of the dynamics of extended spinning compact binaries
A brief review is given of all the Hamiltonians and effective potentials
calculated hitherto covering the post-Newtonian (pN) dynamics of a two body
system. A method is presented to compare (conservative) reduced Hamiltonians
with nonreduced potentials directly at least up to the next-to-leading-pN
order.Comment: Conference proceedings for the 7th International Conference on
Gravitation and Cosmology (ICGC2011), 4 page
Inverse approach to Einstein's equations for fluids with vanishing anisotropic stress tensor
We expand previous work on an inverse approach to Einstein Field Equations
where we include fluids with energy flux and consider the vanishing of the
anisotropic stress tensor. We consider the approach using warped product
spacetimes of class . Although restricted, these spacetimes include many
exact solutions of interest to compact object studies and to cosmological
models studies. The question explored here is as follows: given a spacetime
metric, what fluid flow (timelike congruence), if any, could generate the
spacetime via Einstein's equations. We calculate the flow from the condition of
a vanishing anisotropic stress tensor and give results in terms of the metric
functions in the three canonical types of coordinates. A condition for perfect
fluid sources is also provided. The framework developed is algorithmic and
suited for the study and validation of exact solutions using computer algebra
systems. The framework can be applied to solutions in comoving and non-comoving
frames of reference, and examples in different types of coordinates are worked
out.Comment: 15 pages, matches version to appear in Phys.Rev.
Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin-orbit and leading order in spin(1)-spin(2) and spin-squared couplings
A quasi-Keplerian parameterisation for the solutions of second post-Newtonian
(PN) accurate equations of motion for spinning compact binaries is obtained
including leading order spin-spin and next-to-leading order spin-orbit
interactions. Rotational deformation of the compact objects is incorporated.
For arbitrary mass ratios the spin orientations are taken to be parallel or
anti-parallel to the orbital angular momentum vector. The emitted gravitational
wave forms are given in analytic form up to 2PN point particle, 1.5PN spin
orbit and 1PN spin-spin contributions, where the spins are counted of 0PN
order.Comment: 26 pages, 1 figure, published in CQG. Current version: we removed a
remark and clarified the derivation of the orbital element \e_ph
Exact Solution for the Exterior Field of a Rotating Neutron Star
A four-parameter class of exact asymptotically flat solutions of the
Einstein-Maxwell equations involving only rational functions is presented. It
is able to describe the exterior field of a slowly or rapidly rotating neutron
star with poloidal magnetic field.Comment: Accepted for publication in Phys. Rev. D as Rapid Communication. 8
pages, 2 eps figure
Radiative falloff in Einstein-Straus spacetime
The Einstein-Straus spacetime describes a nonrotating black hole immersed in
a matter-dominated cosmology. It is constructed by scooping out a spherical
ball of the dust and replacing it with a vacuum region containing a black hole
of the same mass. The metric is smooth at the boundary, which is comoving with
the rest of the universe. We study the evolution of a massless scalar field in
the Einstein-Straus spacetime, with a special emphasis on its late-time
behavior. This is done by numerically integrating the scalar wave equation in a
double-null coordinate system that covers both portions (vacuum and dust) of
the spacetime. We show that the field's evolution is governed mostly by the
strong concentration of curvature near the black hole, and the discontinuity in
the dust's mass density at the boundary; these give rise to a rather complex
behavior at late times. Contrary to what it would do in an asymptotically-flat
spacetime, the field does not decay in time according to an inverse power-law.Comment: ReVTeX, 12 pages, 14 figure
An inverse approach to Einstein's equations for non-conducting fluids
We show that a flow (timelike congruence) in any type warped product
spacetime is uniquely and algorithmically determined by the condition of zero
flux. (Though restricted, these spaces include many cases of interest.) The
flow is written out explicitly for canonical representations of the spacetimes.
With the flow determined, we explore an inverse approach to Einstein's
equations where a phenomenological fluid interpretation of a spacetime follows
directly from the metric irrespective of the choice of coordinates. This
approach is pursued for fluids with anisotropic pressure and shear viscosity.
In certain degenerate cases this interpretation is shown to be generically not
unique. The framework developed allows the study of exact solutions in any
frame without transformations. We provide a number of examples, in various
coordinates, including spacetimes with and without unique interpretations. The
results and algorithmic procedure developed are implemented as a computer
algebra program called GRSource.Comment: 9 pages revtex4. Final form to appear in Phys Rev
Radiative falloff in Schwarzschild-de Sitter spacetime
We consider the time evolution of a scalar field propagating in
Schwarzschild-de Sitter spacetime. At early times, the field behaves as if it
were in pure Schwarzschild spacetime; the structure of spacetime far from the
black hole has no influence on the evolution. In this early epoch, the field's
initial outburst is followed by quasi-normal oscillations, and then by an
inverse power-law decay. At intermediate times, the power-law behavior gives
way to a faster, exponential decay. At late times, the field behaves as if it
were in pure de Sitter spacetime; the structure of spacetime near the black
hole no longer influences the evolution in a significant way. In this late
epoch, the field's behavior depends on the value of the curvature-coupling
constant xi. If xi is less than a critical value 3/16, the field decays
exponentially, with a decay constant that increases with increasing xi. If xi >
3/16, the field oscillates with a frequency that increases with increasing xi;
the amplitude of the field still decays exponentially, but the decay constant
is independent of xi.Comment: 10 pages, ReVTeX, 5 figures, references updated, and new section
adde
Mapping spacetimes with LISA: inspiral of a test-body in a `quasi-Kerr' field
The future LISA detector will constitute the prime instrument for
high-precision gravitational wave observations.LISA is expected to provide
information for the properties of spacetime in the vicinity of massive black
holes which reside in galactic nuclei.Such black holes can capture stellar-mass
compact objects, which afterwards slowly inspiral,radiating gravitational
waves.The body's orbital motion and the associated waveform carry information
about the spacetime metric of the massive black hole,and it is possible to
extract this information and experimentally identify (or not!) a Kerr black
hole.In this paper we lay the foundations for a practical `spacetime-mapping'
framework. Our work is based on the assumption that the massive body is not
necessarily a Kerr black hole, and that the vacuum exterior spacetime is
stationary axisymmetric,described by a metric which deviates slightly from the
Kerr metric. We first provide a simple recipe for building such a `quasi-Kerr'
metric by adding to the Kerr metric the deviation in the value of the
quadrupole moment. We then study geodesic motion in this metric,focusing on
equatorial orbits. We proceed by computing `kludge' waveforms which we compare
with their Kerr counterparts. We find that a modest deviation from the Kerr
metric is sufficient for producing a significant mismatch between the
waveforms, provided we fix the orbital parameters. This result suggests that an
attempt to use Kerr waveform templates for studying EMRIs around a non-Kerr
object might result in serious loss of signal-to-noise ratio and total number
of detected events. The waveform comparisons also unveil a `confusion' problem,
that is the possibility of matching a true non-Kerr waveform with a Kerr
template of different orbital parameters.Comment: 19 pages, 6 figure
Radiative falloff of a scalar field in a weakly curved spacetime without symmetries
We consider a massless scalar field propagating in a weakly curved spacetime
whose metric is a solution to the linearized Einstein field equations. The
spacetime is assumed to be stationary and asymptotically flat, but no other
symmetries are imposed -- the spacetime can rotate and deviate strongly from
spherical symmetry. We prove that the late-time behavior of the scalar field is
identical to what it would be in a spherically-symmetric spacetime: it decays
in time according to an inverse power-law, with a power determined by the
angular profile of the initial wave packet (Price falloff theorem). The field's
late-time dynamics is insensitive to the nonspherical aspects of the metric,
and it is governed entirely by the spacetime's total gravitational mass; other
multipole moments, and in particular the spacetime's total angular momentum, do
not enter in the description of the field's late-time behavior. This extended
formulation of Price's falloff theorem appears to be at odds with previous
studies of radiative decay in the spacetime of a Kerr black hole. We show,
however, that the contradiction is only apparent, and that it is largely an
artifact of the Boyer-Lindquist coordinates adopted in these studies.Comment: 17 pages, RevTeX
Nodal and Periastron Precession of Inclined Orbits in the Field of a Rapidly Rotating Neutron Star
We derive a formula for the nodal precession frequency and the Keplerian
period of a particle at an arbitrarily inclined orbit (with a minimum
latitudinal angle reached at the orbit) in the post-Newtonian approximation in
the external field of an oblate rotating neutron star (NS). We also derive
formulas for the nodal precession and periastron rotation frequencies of
slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS
in the form of asymptotic expansions whose first terms are given by the
Okazaki--Kato formulas. The NS gravitational field is described by the exact
solution of the Einstein equation that includes the NS quadrupole moment
induced by rapid rotation. Convenient asymptotic formulas are given for the
metric coefficients of the corresponding space-time in the form of Kerr metric
perturbations in Boyer--Lindquist coordinates.Comment: 12 page