922 research outputs found
k-Inflation
It is shown that a large class of higher-order (i.e. non-quadratic) scalar
kinetic terms can, without the help of potential terms, drive an inflationary
evolution starting from rather generic initial conditions. In many models, this
kinetically driven inflation (or "k-inflation" for short) rolls slowly from a
high-curvature initial phase, down to a low-curvature phase and can exit
inflation to end up being radiation-dominated, in a naturally graceful manner.
We hope that this novel inflation mechanism might be useful in suggesting new
ways of reconciling the string dilaton with inflation.Comment: LaTeX, 20 pages including 3 figures. Submitted to Phys. Lett.
Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
Dimensional regularization is used to derive the equations of motion of two
point masses in harmonic coordinates. At the third post-Newtonian (3PN)
approximation, it is found that the dimensionally regularized equations of
motion contain a pole part [proportional to 1/(d-3)] which diverges as the
space dimension d tends to 3. It is proven that the pole part can be
renormalized away by introducing suitable shifts of the two world-lines
representing the point masses, and that the same shifts renormalize away the
pole part of the "bulk" metric tensor g_munu(x). The ensuing, finite
renormalized equations of motion are then found to belong to the general
parametric equations of motion derived by an extended Hadamard regularization
method, and to uniquely determine the heretofore unknown 3PN parameter lambda
to be: lambda = - 1987/3080. This value is fully consistent with the recent
determination of the equivalent 3PN static ambiguity parameter, omega_s = 0, by
a dimensional-regularization derivation of the Hamiltonian in
Arnowitt-Deser-Misner coordinates. Our work provides a new, powerful check of
the consistency of the dimensional regularization method within the context of
the classical gravitational interaction of point particles.Comment: 82 pages, LaTeX 2e, REVTeX 4, 8 PostScript figures, minor changes to
reflect Phys. Rev. D versio
Chaos and Order in Models of Black Hole Pairs
Chaos in the orbits of black hole pairs has by now been confirmed by several
independent groups. While the chaotic behavior of binary black hole orbits is
no longer argued, it remains difficult to quantify the importance of chaos to
the evolutionary dynamics of a pair of comparable mass black holes. None of our
existing approximations are robust enough to offer convincing quantitative
conclusions in the most highly nonlinear regime. It is intriguing to note that
in three different approximations to a black hole pair built of a spinning
black hole and a non-spinning companion, two approximations exhibit chaos and
one approximation does not. The fully relativistic scenario of a spinning
test-mass around a Schwarzschild black hole shows chaos, as does the
Post-Newtonian Lagrangian approximation. However, the approximately equivalent
Post-Newtonian Hamiltonian approximation does not show chaos when only one body
spins. It is well known in dynamical systems theory that one system can be
regular while an approximately related system is chaotic, so there is no formal
conflict. However,the physical question remains, Is there chaos for comparable
mass binaries when only one object spins? We are unable to answer this question
given the poor convergence of the Post-Newtonian approximation to the fully
relativistic system. A resolution awaits better approximations that can be
trusted in the highly nonlinear regime
Effective field theory calculation of second post-Newtonian binary dynamics
We use the effective field theory for gravitational bound states, proposed by
Goldberger and Rothstein, to compute the interaction Lagrangian of a binary
system at the second Post-Newtonian order. Throughout the calculation, we use a
metric parametrization based on a temporal Kaluza-Klein decomposition and test
the claim by Kol and Smolkin that this parametrization provides important
calculational advantages. We demonstrate how to use the effective field theory
method efficiently in precision calculations, and we reproduce known results
for the second Post-Newtonian order equations of motion in harmonic gauge in a
straightforward manner.Comment: Replaced with published versio
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
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
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.
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
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.
Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit
We report our rederivation of the equations of motion for relativistic
compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order
approximation to general relativity using the strong field point particle limit
to describe self-gravitating stars instead of the Dirac delta functional. The
computation is done in harmonic coordinates. Our equations of motion describe
the orbital motion of the binary consisting of spherically symmetric
non-rotating stars. The resulting equations of motion fully agree with the 3.5
PN equations of motion derived in the previous works. We also show that the
locally defined energy of the star has a simple relation with its mass up to
the 3.5 PN order.Comment: 38 pages, no figures. Accepted for publication in Phys. Rev.
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