341 research outputs found
A Linear-Nonlinear Formulation of Einstein Equations for the Two-Body Problem in General Relativity
A formulation of Einstein equations is presented that could yield advantages
in the study of collisions of binary compact objects during regimes between
linear-nonlinear transitions. The key idea behind this formulation is a
separation of the dynamical variables into i) a fixed conformal 3-geometry, ii)
a conformal factor possessing nonlinear dynamics and iii) transverse-traceless
perturbations of the conformal 3-geometry.Comment: 7 pages, no figure
Mode coupling in the nonlinear response of black holes
We study the properties of the outgoing gravitational wave produced when a
non-spinning black hole is excited by an ingoing gravitational wave.
Simulations using a numerical code for solving Einstein's equations allow the
study to be extended from the linearized approximation, where the system is
treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime.
Several nonlinear features are found which bear importance to the data analysis
of gravitational waves. When compared to the results obtained in the linearized
approximation, we observe large phase shifts, a stronger than linear generation
of gravitational wave output and considerable generation of radiation in
polarization states which are not found in the linearized approximation. In
terms of a spherical harmonic decomposition, the nonlinear properties of the
harmonic amplitudes have simple scaling properties which offer an economical
way to catalog the details of the waves produced in such black hole processes.Comment: 17 pages, 20 figures, abstract and introduction re-writte
Binary black hole initial data for numerical general relativity based on post-Newtonian data
With the goal of taking a step toward the construction of astrophysically
realistic initial data for numerical simulations of black holes, we for the
first time derive a family of fully general relativistic initial data based on
post-2-Newtonian expansions of the 3-metric and extrinsic curvature without
spin. It is expected that such initial data provide a direct connection with
the early inspiral phase of the binary system. We discuss a straightforward
numerical implementation, which is based on a generalized puncture method.
Furthermore, we suggest a method to address some of the inherent ambiguity in
mapping post-Newtonian data onto a solution of the general relativistic
constraints.Comment: 13 pages, 8 figures, RevTex
Fluctuations of an evaporating black hole from back reaction of its Hawking radiation: Questioning a premise in earlier work
This paper delineates the first steps in a systematic quantitative study of
the spacetime fluctuations induced by quantum fields in an evaporating black
hole. We explain how the stochastic gravity formalism can be a useful tool for
that purpose within a low-energy effective field theory approach to quantum
gravity. As an explicit example we apply it to the study of the
spherically-symmetric sector of metric perturbations around an evaporating
black hole background geometry. For macroscopic black holes we find that those
fluctuations grow and eventually become important when considering sufficiently
long periods of time (of the order of the evaporation time), but well before
the Planckian regime is reached. In addition, the assumption of a simple
correlation between the fluctuations of the energy flux crossing the horizon
and far from it, which was made in earlier work on spherically-symmetric
induced fluctuations, is carefully analyzed and found to be invalid. Our
analysis suggests the existence of an infinite amplitude for the fluctuations
of the horizon as a three-dimensional hypersurface. We emphasize the need for
understanding and designing operational ways of probing quantum metric
fluctuations near the horizon and extracting physically meaningful information.Comment: 10 pages, REVTeX; minor changes, a few references added and a brief
discussion of their relevance included. To appear in the proceedings of the
10th Peyresq meeting. Dedicated to Rafael Sorkin on the occasion of his 60th
birthda
Towards a Realistic Neutron Star Binary Inspiral: Initial Data and Multiple Orbit Evolution in Full General Relativity
This paper reports on our effort in modeling realistic astrophysical neutron
star binaries in general relativity. We analyze under what conditions the
conformally flat quasiequilibrium (CFQE) approach can generate
``astrophysically relevant'' initial data, by developing an analysis that
determines the violation of the CFQE approximation in the evolution of the
binary described by the full Einstein theory. We show that the CFQE assumptions
significantly violate the Einstein field equations for corotating neutron stars
at orbital separations nearly double that of the innermost stable circular
orbit (ISCO) separation, thus calling into question the astrophysical relevance
of the ISCO determined in the CFQE approach. With the need to start numerical
simulations at large orbital separation in mind, we push for stable and long
term integrations of the full Einstein equations for the binary neutron star
system. We demonstrate the stability of our numerical treatment and analyze the
stringent requirements on resolution and size of the computational domain for
an accurate simulation of the system.Comment: 22 pages, 18 figures, accepted to Phys. Rev.
Circular orbits of corotating binary black holes: comparison between analytical and numerical results
We compare recent numerical results, obtained within a ``helical Killing
vector'' (HKV) approach, on circular orbits of corotating binary black holes to
the analytical predictions made by the effective one body (EOB) method (which
has been recently extended to the case of spinning bodies). On the scale of the
differences between the results obtained by different numerical methods, we
find good agreement between numerical data and analytical predictions for
several invariant functions describing the dynamical properties of circular
orbits. This agreement is robust against the post-Newtonian accuracy used for
the analytical estimates, as well as under choices of resummation method for
the EOB ``effective potential'', and gets better as one uses a higher
post-Newtonian accuracy. These findings open the way to a significant
``merging'' of analytical and numerical methods, i.e. to matching an EOB-based
analytical description of the (early and late) inspiral, up to the beginning of
the plunge, to a numerical description of the plunge and merger. We illustrate
also the ``flexibility'' of the EOB approach, i.e. the possibility of
determining some ``best fit'' values for the analytical parameters by
comparison with numerical data.Comment: Minor revisions, accepted for publication in Phys. Rev. D, 19 pages,
6 figure
Cosmological Evolution of Brane World Moduli
We study cosmological consequences of non-constant brane world moduli in five
dimensional brane world models with bulk scalars and two boundary branes. We
focus on the case where the brane tension is an exponential function of the
bulk scalar field, . In the limit , the model reduces to the two-brane model of Randall-Sundrum, whereas larger
values of allow for a less warped bulk geometry. Using the moduli
space approximation, we derive the four-dimensional low-energy effective action
from a supergravity-inspired five-dimensional theory. For arbitrary values of
, the resulting theory has the form of a bi-scalar-tensor theory. We
show that, in order to be consistent with local gravitational observations,
has to be small (less than ) and the separation of the branes
must be large. We study the cosmological evolution of the interbrane distance
and the bulk scalar field for different matter contents on each branes. Our
findings indicate that attractor solutions exist which drive the moduli fields
towards values consistent with observations. The efficiency of the attractor
mechanism crucially depends on the matter content on each branes. In the
five-dimensional description, the attractors correspond to the motion of the
negative tension brane towards a bulk singularity, which signals the eventual
breakdown of the four-dimensional description and the necessity of a better
understanding of the bulk singularity.Comment: 18 pages, 10 figures, typos and factor of 2 corrected, version to
appear in Physical Review
Linear Response, Validity of Semi-Classical Gravity, and the Stability of Flat Space
A quantitative test for the validity of the semi-classical approximation in
gravity is given. The criterion proposed is that solutions to the
semi-classical Einstein equations should be stable to linearized perturbations,
in the sense that no gauge invariant perturbation should become unbounded in
time. A self-consistent linear response analysis of these perturbations, based
upon an invariant effective action principle, necessarily involves metric
fluctuations about the mean semi-classical geometry, and brings in the
two-point correlation function of the quantum energy-momentum tensor in a
natural way. This linear response equation contains no state dependent
divergences and requires no new renormalization counterterms beyond those
required in the leading order semi-classical approximation. The general linear
response criterion is applied to the specific example of a scalar field with
arbitrary mass and curvature coupling in the vacuum state of Minkowski
spacetime. The spectral representation of the vacuum polarization function is
computed in n dimensional Minkowski spacetime, and used to show that the flat
space solution to the semi-classical Einstein equations for n=4 is stable to
all perturbations on distance scales much larger than the Planck length.Comment: 22 pages: This is a significantly expanded version of gr-qc/0204083,
with two additional sections and two new appendices giving a complete,
explicit example of the semi-classical stability criterion proposed in the
previous pape
On gravitational waves emitted by an ensemble of rotating neutron stars
We study the possibility to detect the gravitational wave background
generated by all the neutron stars in the Galaxy with only one gravitational
wave interferometric detector. The proposed strategy consists in squaring the
detector's output and searching for a sidereal modulation. The shape of the
squared signal is computed for a disk and a halo distribution of neutron stars.
The required noise stability of the interferometric detector is discussed. We
argue that a possible population of old neutron stars, originating from a high
stellar formation rate at the birth of the Galaxy and not emitting as radio
pulsars, could be detected by the proposed technique in the low frequency range
of interferometric experiments.Comment: 14 pages, 2 PostScript figures, RevTeX, accepted for publication in
Physical Review
Detector Description and Performance for the First Coincidence Observations between LIGO and GEO
For 17 days in August and September 2002, the LIGO and GEO interferometer
gravitational wave detectors were operated in coincidence to produce their
first data for scientific analysis. Although the detectors were still far from
their design sensitivity levels, the data can be used to place better upper
limits on the flux of gravitational waves incident on the earth than previous
direct measurements. This paper describes the instruments and the data in some
detail, as a companion to analysis papers based on the first data.Comment: 41 pages, 9 figures 17 Sept 03: author list amended, minor editorial
change
- âŠ