598 research outputs found
Post-Newtonian Theory for Precision Doppler Measurements of Binary Star Orbits
The determination of velocities of stars from precise Doppler measurements is
described here using relativistic theory of astronomical reference frames so as
to determine the Keplerian and post-Keplerian parameters of binary systems. We
apply successive Lorentz transformations and the relativistic equation of light
propagation to establish the exact treatment of Doppler effect in binary
systems both in special and general relativity theories. As a result, the
Doppler shift is a sum of (1) linear in terms, which include the
ordinary Doppler effect and its variation due to the secular radial
acceleration of the binary with respect to observer; (2) terms proportional to
, which include the contributions from the quadratic Doppler effect
caused by the relative motion of binary star with respect to the Solar system,
motion of the particle emitting light and diurnal rotational motion of
observer, orbital motion of the star around the binary's barycenter, and
orbital motion of the Earth; and (3) terms proportional to , which
include the contributions from redshifts due to gravitational fields of the
star, star's companion, Galaxy, Solar system, and the Earth. After
parameterization of the binary's orbit we find that the presence of
periodically changing terms in the Doppler schift enables us disentangling
different terms and measuring, along with the well known Keplerian parameters
of the binary, four additional post-Keplerian parameters, including the
inclination angle of the binary's orbit, . We briefly discuss feasibility of
practical implementation of these theoretical results, which crucially depends
on further progress in the technique of precision Doppler measurements.Comment: Minor changes, 1 Figure included, submitted to Astrophys.
Self-consistency of relativistic observables with general relativity in the white dwarf-neutron star binary pulsar PSR J1141-6545
Here we report timing measurements of the relativistic binary pulsar PSR
J1141-6545 that constrain the component masses and demonstrate that the orbital
period derivative \dot Pb = (-4+/-1)x10^-13 is consistent with gravitational
wave emission as described by the general theory of relativity. The mass of the
neutron star and its companion are 1.30+/-0.02 Mo and 0.986+/-0.020 Mo
respectively, suggesting a white dwarf companion, and extending the range of
systems for which general relativity provides a correct description. On
evolutionary grounds, the progenitor mass of PSR J1141-6545 should be near the
minimum for neutron star production. Its mass is two standard deviations below
the mean of the other neutron stars, suggesting a relationship between
progenitor and remnant masses.Comment: 10 pages, 2 figures, revised version to Ap J Letter
On the equation of motion of compact binaries in Post-Newtonian approximation
A third post-Newtonian (3 PN) equation of motion for two spherical compact
stars in a harmonic coordinate has been derived based on the surface integral
approach and the strong field point particle limit. The strong field point
particle limit enables us to incorporate a notion of a self-gravitating regular
star into general relativity. The resulting 3 PN equation of motion is Lorentz
invariant, unambiguous, and conserves an energy of the binary orbital motion.Comment: 7 pages, no figure. Proceedings of the 5th Amaldi Conference on
Gravitational Waves, Pisa, Italy, 6-11 July 200
Gravitational-wave versus binary-pulsar tests of strong-field gravity
Binary systems comprising at least one neutron star contain strong
gravitational field regions and thereby provide a testing ground for
strong-field gravity. Two types of data can be used to test the law of gravity
in compact binaries: binary pulsar observations, or forthcoming
gravitational-wave observations of inspiralling binaries. We compare the
probing power of these two types of observations within a generic two-parameter
family of tensor-scalar gravitational theories. Our analysis generalizes
previous work (by us) on binary-pulsar tests by using a sample of realistic
equations of state for nuclear matter (instead of a polytrope), and goes beyond
a previous study (by C.M. Will) of gravitational-wave tests by considering more
general tensor-scalar theories than the one-parameter Jordan-Fierz-Brans-Dicke
one. Finite-size effects in tensor-scalar gravity are also discussed.Comment: 23 pages, REVTeX 3.0, uses epsf.tex to include 5 postscript figures
(2 paragraphs and a 5th figure added at the end of section IV + minor
changes
The Equivalence Principle and the Constants of Nature
We briefly review the various contexts within which one might address the
issue of ``why'' the dimensionless constants of Nature have the particular
values that they are observed to have. Both the general historical trend, in
physics, of replacing a-priori-given, absolute structures by dynamical
entities, and anthropic considerations, suggest that coupling ``constants''
have a dynamical nature. This hints at the existence of observable violations
of the Equivalence Principle at some level, and motivates the need for improved
tests of the Equivalence Principle.Comment: 12 pages; invited talk at the ISSI Workshop on the Nature of Gravity:
Confronting Theory and Experiment in Space, Bern, Switzerland, 6-10 October
2008; to appear in Space Science Review
Sugawara-type constraints in hyperbolic coset models
In the conjectured correspondence between supergravity and geodesic models on
infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the
constraints play a central role. We present a Sugawara-type construction in
terms of the E10 Noether charges that extends these constraints infinitely into
the hyperbolic algebra, in contrast to the truncated expressions obtained in
arXiv:0709.2691 that involved only finitely many generators. Our extended
constraints are associated to an infinite set of roots which are all imaginary,
and in fact fill the closed past light-cone of the Lorentzian root lattice. The
construction makes crucial use of the E10 Weyl group and of the fact that the
E10 model contains both D=11 supergravity and D=10 IIB supergravity. Our
extended constraints appear to unite in a remarkable manner the different
canonical constraints of these two theories. This construction may also shed
new light on the issue of `open constraint algebras' in traditional canonical
approaches to gravity.Comment: 49 page
Coalescence of Two Spinning Black Holes: An Effective One-Body Approach
We generalize to the case of spinning black holes a recently introduced
``effective one-body'' approach to the general relativistic dynamics of binary
systems. The combination of the effective one-body approach, and of a Pad\'e
definition of some crucial effective radial functions, is shown to define a
dynamics with much improved post-Newtonian convergence properties, even for
black hole separations of the order of . We discuss the approximate
existence of a two-parameter family of ``spherical orbits'' (with constant
radius), and, of a corresponding one-parameter family of ``last stable
spherical orbits'' (LSSO). These orbits are of special interest for forthcoming
LIGO/VIRGO/GEO gravitational wave observations. It is argued that for most (but
not all) of the parameter space of two spinning holes the effective one-body
approach gives a reliable analytical tool for describing the dynamics of the
last orbits before coalescence. This tool predicts, in a quantitative way, how
certain spin orientations increase the binding energy of the LSSO. This leads
to a detection bias, in LIGO/VIRGO/GEO observations, favouring spinning black
hole systems, and makes it urgent to complete the conservative effective
one-body dynamics given here by adding (resummed) radiation reaction effects,
and by constructing gravitational waveform templates that include spin effects.
Finally, our approach predicts that the spin of the final hole formed by the
coalescence of two arbitrarily spinning holes never approaches extremality.Comment: 26 pages, two eps figures, accepted in Phys. Rev. D, minor updating
of the text, clarifications added and inclusion of a few new reference
Second post-Newtonian gravitational wave polarizations for compact binaries in elliptical orbits
The second post-Newtonian (2PN) contribution to the `plus' and `cross'
gravitational wave polarizations associated with gravitational radiation from
non-spinning, compact binaries moving in elliptic orbits is computed. The
computation starts from our earlier results on 2PN generation, crucially
employs the 2PN accurate generalized quasi-Keplerian parametrization of
elliptic orbits by Damour, Sch\"afer and Wex and provides 2PN accurate
expressions modulo the tail terms for gravitational wave polarizations
incorporating effects of eccentricity and periastron precession.Comment: 40 pages, 10 figures, To appear in Phys. Rev.
Relativistic theory of elastic deformable astronomical bodies: perturbation equations in rotating spherical coordinates and junction conditions
In this paper, the dynamical equations and junction conditions at the
interface between adjacent layers of different elastic properties for an
elastic deformable astronomical body in the first post-Newtonian approximation
of Einstein theory of gravity are discussed in both rotating Cartesian
coordinates and rotating spherical coordinates. The unperturbed rotating body
(the ground state) is described as uniformly rotating, stationary and
axisymmetric configuration in an asymptotically flat space-time manifold.
Deviations from the equilibrium configuration are described by means of a
displacement field. In terms of the formalism of relativistic celestial
mechanics developed by Damour, Soffel and Xu, and the framework established by
Carter and Quintana the post Newtonian equations of the displacement field and
the symmetric trace-free shear tensor are obtained. Corresponding
post-Newtonian junction conditions at interfaces also the outer surface
boundary conditions are presented. The PN junction condition is an extension of
Wahr's one which is a Newtonian junction conditions without rotating.Comment: Revtex4, 14 page
General relativistic dynamics of compact binaries at the third post-Newtonian order
The general relativistic corrections in the equations of motion and
associated energy of a binary system of point-like masses are derived at the
third post-Newtonian (3PN) order. The derivation is based on a post-Newtonian
expansion of the metric in harmonic coordinates at the 3PN approximation. The
metric is parametrized by appropriate non-linear potentials, which are
evaluated in the case of two point-particles using a Lorentzian version of an
Hadamard regularization which has been defined in previous works.
Distributional forms and distributional derivatives constructed from this
regularization are employed systematically. The equations of motion of the
particles are geodesic-like with respect to the regularized metric. Crucial
contributions to the acceleration are associated with the non-distributivity of
the Hadamard regularization and the violation of the Leibniz rule by the
distributional derivative. The final equations of motion at the 3PN order are
invariant under global Lorentz transformations, and admit a conserved energy
(neglecting the radiation reaction force at the 2.5PN order). However, they are
not fully determined, as they depend on one arbitrary constant, which reflects
probably a physical incompleteness of the point-mass regularization. The
results of this paper should be useful when comparing theory to the
observations of gravitational waves from binary systems in future detectors
VIRGO and LIGO.Comment: 78 pages, submitted to Phys. Rev. D, with minor modification
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