363 research outputs found
Truncated post-Newtonian neutron star model
As a preliminary step towards simulating binary neutron star coalescing
problem, we test a post-Newtonian approach by constructing a single neutron
star model. We expand the Tolman-Oppenheimer-Volkov equation of hydrostatic
equilibrium by the power of , where is the speed of light, and
truncate at the various order. We solve the system using the polytropic
equation of state with index and 3, and show how this
approximation converges together with mass-radius relations. Next, we solve the
Hamiltonian constraint equation with these density profiles as trial functions,
and examine the differences in the final metric. We conclude the second
`post-Newtonian' approximation is close enough to describe general relativistic
single star. The result of this report will be useful for further binary
studies.
(Note to readers) This paper was accepted for publication in Physical Review
D. [access code dsj637]. However, since I was strongly suggested that the
contents of this paper should be included as a section in our group's future
paper, I gave up the publication.Comment: 5 pages, RevTeX, 3 eps figs, epsf.sty, accepted for publication in
PRD (Brief Report), but will not appea
Laser Interferometric Detectors of Gravitational Waves
A laser interferometric detector of gravitational waves is studied and a
complete solution (to first order in the metric perturbation) of the coupled
Einstein-Maxwell equations with appropriate boundary conditions for the light
beams is determined. The phase shift, the light deflection and the rotation of
the polarization axis induced by gravitational waves are computed. The results
are compared with previous literature, and are shown to hold also for detectors
which are large in comparison with the gravitational wavelength.Comment: 13 pages, LaTe
Matter flows around black holes and gravitational radiation
We develop and calibrate a new method for estimating the gravitational
radiation emitted by complex motions of matter sources in the vicinity of black
holes. We compute numerically the linearized curvature perturbations induced by
matter fields evolving in fixed black hole backgrounds, whose evolution we
obtain using the equations of relativistic hydrodynamics. The current
implementation of the proposal concerns non-rotating holes and axisymmetric
hydrodynamical motions. As first applications we study i) dust shells falling
onto the black hole isotropically from finite distance, ii) initially spherical
layers of material falling onto a moving black hole, and iii) anisotropic
collapse of shells. We focus on the dependence of the total gravitational wave
energy emission on the flow parameters, in particular shell thickness, velocity
and degree of anisotropy. The gradual excitation of the black hole quasi-normal
mode frequency by sufficiently compact shells is demonstrated and discussed. A
new prescription for generating physically reasonable initial data is
discussed, along with a range of technical issues relevant to numerical
relativity.Comment: 27 pages, 12 encapsulated figures, revtex, amsfonts, submitted to
Phys. Rev.
Momentum constraint relaxation
Full relativistic simulations in three dimensions invariably develop runaway
modes that grow exponentially and are accompanied by violations of the
Hamiltonian and momentum constraints. Recently, we introduced a numerical
method (Hamiltonian relaxation) that greatly reduces the Hamiltonian constraint
violation and helps improve the quality of the numerical model. We present here
a method that controls the violation of the momentum constraint. The method is
based on the addition of a longitudinal component to the traceless extrinsic
curvature generated by a vector potential w_i, as outlined by York. The
components of w_i are relaxed to solve approximately the momentum constraint
equations, pushing slowly the evolution toward the space of solutions of the
constraint equations. We test this method with simulations of binary neutron
stars in circular orbits and show that effectively controls the growth of the
aforementioned violations. We also show that a full numerical enforcement of
the constraints, as opposed to the gentle correction of the momentum relaxation
scheme, results in the development of instabilities that stop the runs shortly.Comment: 17 pages, 10 figures. New numerical tests and references added. More
detailed description of the algorithms are provided. Final published versio
Hamiltonian Relaxation
Due to the complexity of the required numerical codes, many of the new
formulations for the evolution of the gravitational fields in numerical
relativity are not tested on binary evolutions. We introduce in this paper a
new testing ground for numerical methods based on the simulation of binary
neutron stars. This numerical setup is used to develop a new technique, the
Hamiltonian relaxation (HR), that is benchmarked against the currently most
stable simulations based on the BSSN method. We show that, while the length of
the HR run is somewhat shorter than the equivalent BSSN simulation, the HR
technique improves the overall quality of the simulation, not only regarding
the satisfaction of the Hamiltonian constraint, but also the behavior of the
total angular momentum of the binary. The latest quantity agrees well with
post-Newtonian estimations for point-mass binaries in circular orbits.Comment: More detailed description of the numerical implementation added and
some typos corrected. Version accepted for publication in Class. and Quantum
Gravit
The Collision of Two Black Holes
We study the head-on collision of two equal mass, nonrotating black holes. We
consider a range of cases from holes surrounded by a common horizon to holes
initially separated by about , where is the mass of each hole. We
determine the waveforms and energies radiated for both the and
waves resulting from the collision. In all cases studied the normal
modes of the final black hole dominate the spectrum. We also estimate
analytically the total gravitational radiation emitted, taking into account the
tidal heating of horizons using the membrane paradigm, and other effects. For
the first time we are able to compare analytic calculations, black hole
perturbation theory, and strong field, nonlinear numerical calculations for
this problem, and we find excellent agreement.Comment: 14 pages, 93-
Stable Topologies of Event Horizon
In our previous work, it was shown that the topology of an event horizon (EH)
is determined by the past endpoints of the EH. A torus EH (the collision of two
EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In
the present article, we examine the stability of the topology of the EH. We see
that a simple case of a single spherical EH is unstable. Furthermore, in
general, an EH with handles (a torus, a double torus, ...) is structurally
stable in the sense of catastrophe theory.Comment: 21 pages, revtex, five figures containe
A method for detecting gravitational waves coincident with gamma ray bursts
The mechanism for gamma ray bursters and the detection of gravitational waves
(GWs) are two outstanding problems facing modern physics. Many models of gamma
ray bursters predict copious GW emission, so the assumption of an association
between GWs and GRBs may be testable with existing bar GW detector data. We
consider Weber bar data streams in the vicinity of known GRB times and present
calculations of the expected signal after co-addition of 1000 GW/GRBs that have
been shifted to a common zero time. Our calculations are based on assumptions
concerning the GW spectrum and the redshift distribution of GW/GRB sources
which are consistent with current GW/GRB models. We discuss further
possibilities of GW detection associated with GRBs in light of future bar
detector improvements and suggest that co-addition of data from several
improved bar detectors may result in detection of GWs (if the GW/GRB assumption
is correct) on a time scale comparable with the LIGO projects.Comment: Accepted by MNRAS. 9 pages, 6 ps figures, MNRAS style. Proof
corrections made, accepted versio
Various features of quasiequilibrium sequences of binary neutron stars in general relativity
Quasiequilibrium sequences of binary neutron stars are numerically calculated
in the framework of the Isenberg-Wilson-Mathews (IWM) approximation of general
relativity. The results are presented for both rotation states of synchronized
spins and irrotational motion, the latter being considered as the realistic one
for binary neutron stars just prior to the merger. We assume a polytropic
equation of state and compute several evolutionary sequences of binary systems
composed of different-mass stars as well as identical-mass stars with adiabatic
indices gamma=2.5, 2.25, 2, and 1.8. From our results, we propose as a
conjecture that if the turning point of binding energy (and total angular
momentum) locating the innermost stable circular orbit (ISCO) is found in
Newtonian gravity for some value of the adiabatic index gamma_0, that of the
ADM mass (and total angular momentum) should exist in the IWM approximation of
general relativity for the same value of the adiabatic index.Comment: Text improved, some figures changed or deleted, new table, 38 pages,
31 figures, accepted for publication in Phys. Rev.
Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models
We perform fully relativistic calculations of binary neutron stars in
quasi-equilibrium circular orbits. We integrate Einstein's equations together
with the relativistic equation of hydrostatic equilibrium to solve the initial
value problem for equal-mass binaries of arbitrary separation. We construct
sequences of constant rest mass and identify the innermost stable circular
orbit and its angular velocity. We find that the quasi-equilibrium maximum
allowed mass of a neutron star in a close binary is slightly larger than in
isolation.Comment: 4 pages, 3 figures, RevTe
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