20 research outputs found
Comparing Criteria for Circular Orbits in General Relativity
We study a simple analytic solution to Einstein's field equations describing
a thin spherical shell consisting of collisionless particles in circular orbit.
We then apply two independent criteria for the identification of circular
orbits, which have recently been used in the numerical construction of binary
black hole solutions, and find that both yield equivalent results. Our
calculation illustrates these two criteria in a particularly transparent
framework and provides further evidence that the deviations found in those
numerical binary black hole solutions are not caused by the different criteria
for circular orbits.Comment: 4 pages; to appear in PRD as a Brief Report; added and corrected
reference
Two physical characteristics of numerical apparent horizons
This article translates some recent results on quasilocal horizons into the
language of general relativity so as to make them more useful to
numerical relativists. In particular quantities are described which
characterize how quickly an apparent horizon is evolving and how close it is to
either equilibrium or extremality.Comment: 6 pages, 2 figures, conference proceedings loosely based on talk
given at Theory Canada III (Edmonton, Alberta, 2007). V2: Minor changes in
response to referees comments to improve clarity and fix typos. One reference
adde
Post-Newtonian SPH calculations of binary neutron star coalescence. I. Method and first results
We present the first results from our Post-Newtonian (PN) Smoothed Particle
Hydrodynamics (SPH) code, which has been used to study the coalescence of
binary neutron star (NS) systems. The Lagrangian particle-based code
incorporates consistently all lowest-order (1PN) relativistic effects, as well
as gravitational radiation reaction, the lowest-order dissipative term in
general relativity. We test our code on sequences of single NS models of
varying compactness, and we discuss ways to make PN simulations more relevant
to realistic NS models. We also present a PN SPH relaxation procedure for
constructing equilibrium models of synchronized binaries, and we use these
equilibrium models as initial conditions for our dynamical calculations of
binary coalescence. Though unphysical, since tidal synchronization is not
expected in NS binaries, these initial conditions allow us to compare our PN
work with previous Newtonian results.
We compare calculations with and without 1PN effects, for NS with stiff
equations of state, modeled as polytropes with . We find that 1PN
effects can play a major role in the coalescence, accelerating the final
inspiral and causing a significant misalignment in the binary just prior to
final merging. In addition, the character of the gravitational wave signal is
altered dramatically, showing strong modulation of the exponentially decaying
waveform near the end of the merger. We also discuss briefly the implications
of our results for models of gamma-ray bursts at cosmological distances.Comment: RevTeX, 37 pages, 17 figures, to appear in Phys. Rev. D, minor
corrections onl
Nonlocal Equation of State in Anisotropic Static Fluid Spheres in General Relativity
We show that it is possible to obtain credible static anisotropic spherically
symmetric matter configurations starting from known density profiles and
satisfying a nonlocal equation of state. These particular types of equation of
state describe, at a given point, the components of the corresponding
energy-momentum tensor not only as a function at that point, but as a
functional throughout the enclosed configuration. To establish the physical
plausibility of the proposed family of solutions satisfying nonlocal equation
of state, we study the constraints imposed by the junction and energy
conditions on these bounded matter distributions.
We also show that it is possible to obtain physically plausible static
anisotropic spherically symmetric matter configurations, having nonlocal
equations of state\textit{,}concerning the particular cases where the radial
pressure vanishes and, other where the tangential pressures vanishes. The later
very particular type of relativistic sphere with vanishing tangential stresses
is inspired by some of the models proposed to describe extremely magnetized
neutron stars (magnetars) during the transverse quantum collapse.Comment: 21 pages, 1 figure, minor changes in the text, references added, two
new solutions studie
Computing gravitational waves from slightly nonspherical stellar collapse to black hole: Odd-parity perturbation
Nonspherical stellar collapse to a black hole is one of the most promising
gravitational wave sources for gravitational wave detectors. We numerically
study gravitational waves from a slightly nonspherical stellar collapse to a
black hole in linearized Einstein theory. We adopt a spherically collapsing
star as the zeroth-order solution and gravitational waves are computed using
perturbation theory on the spherical background. In this paper we focus on the
perturbation of odd-parity modes. Using the polytropic equations of state with
polytropic indices and 3, we qualitatively study gravitational waves
emitted during the collapse of neutron stars and supermassive stars to black
holes from a marginally stable equilibrium configuration. Since the matter
perturbation profiles can be chosen arbitrarily, we provide a few types for
them. For , the gravitational waveforms are mainly characterized by a
black hole quasinormal mode ringing, irrespective of perturbation profiles
given initially. However, for , the waveforms depend strongly on the
initial perturbation profiles. In other words, the gravitational waveforms
strongly depend on the stellar configuration and, in turn, on the ad hoc choice
of the functional form of the perturbation in the case of supermassive stars.Comment: 31 pages, accepted for publication in Phys. Rev. D, typos and minor
errors correcte
Dynamics of spherically symmetric spacetimes: hydrodynamics and radiation
Using the 3+1 formalism of general relativity we obtain the equations
governing the dynamics of spherically symmetric spacetimes with arbitrary
sources. We then specialize for the case of perfect fluids accompanied by a
flow of interacting massless or massive particles (e.g. neutrinos) which are
described in terms of relativistic transport theory. We focus in three types of
coordinates: 1) isotropic gauge and maximal slicing, 2) radial gauge and polar
slicing, and 3) isotropic gauge and polar slicing.Comment: submitted to Phys. Rev. D, 46 pages, RevTex file, no figure
Relativistic Hydrodynamic Evolutions with Black Hole Excision
We present a numerical code designed to study astrophysical phenomena
involving dynamical spacetimes containing black holes in the presence of
relativistic hydrodynamic matter. We present evolutions of the collapse of a
fluid star from the onset of collapse to the settling of the resulting black
hole to a final stationary state. In order to evolve stably after the black
hole forms, we excise a region inside the hole before a singularity is
encountered. This excision region is introduced after the appearance of an
apparent horizon, but while a significant amount of matter remains outside the
hole. We test our code by evolving accurately a vacuum Schwarzschild black
hole, a relativistic Bondi accretion flow onto a black hole, Oppenheimer-Snyder
dust collapse, and the collapse of nonrotating and rotating stars. These
systems are tracked reliably for hundreds of M following excision, where M is
the mass of the black hole. We perform these tests both in axisymmetry and in
full 3+1 dimensions. We then apply our code to study the effect of the stellar
spin parameter J/M^2 on the final outcome of gravitational collapse of rapidly
rotating n = 1 polytropes. We find that a black hole forms only if J/M^2<1, in
agreement with previous simulations. When J/M^2>1, the collapsing star forms a
torus which fragments into nonaxisymmetric clumps, capable of generating
appreciable ``splash'' gravitational radiation.Comment: 17 pages, 14 figures, submitted to PR
Jacobi-like bar mode instability of relativistic rotating bodies
We perform some numerical study of the secular triaxial instability of
rigidly rotating homogeneous fluid bodies in general relativity. In the
Newtonian limit, this instability arises at the bifurcation point between the
Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by
viscous dissipation. We locate the onset of instability along several constant
baryon mass sequences of uniformly rotating axisymmetric bodies for compaction
parameter . We find that general relativity weakens the Jacobi
like bar mode instability, but the stabilizing effect is not very strong.
According to our analysis the critical value of the ratio of the kinetic energy
to the absolute value of the gravitational potential energy for compaction parameter as high as 0.275 is only 30% higher than the
Newtonian value. The critical value of the eccentricity depends very weakly on
the degree of relativity and for is only 2% larger than the
Newtonian value at the onset for the secular bar mode instability. We compare
our numerical results with recent analytical investigations based on the
post-Newtonian expansion.Comment: 15 pages, 8 figures, submitted to Phys. Rev.
Post-Newtonian SPH calculations of binary neutron star coalescence. II. Binary mass ratio, equation of state, and spin dependence
Using our new Post-Newtonian SPH (smoothed particle hydrodynamics) code, we
study the final coalescence and merging of neutron star (NS) binaries. We vary
the stiffness of the equation of state (EOS) as well as the initial binary mass
ratio and stellar spins. Results are compared to those of Newtonian
calculations, with and without the inclusion of the gravitational radiation
reaction. We find a much steeper decrease in the gravity wave peak strain and
luminosity with decreasing mass ratio than would be predicted by simple
point-mass formulae. For NS with softer EOS (which we model as simple
polytropes) we find a stronger gravity wave emission, with a
different morphology than for stiffer EOS (modeled as polytropes as
in our previous work). We also calculate the coalescence of NS binaries with an
irrotational initial condition, and find that the gravity wave signal is
relatively suppressed compared to the synchronized case, but shows a very
significant second peak of emission. Mass shedding is also greatly reduced, and
occurs via a different mechanism than in the synchronized case. We discuss the
implications of our results for gravity wave astronomy with laser
interferometers such as LIGO, and for theoretical models of gamma-ray bursts
(GRBs) based on NS mergers.Comment: RevTeX, 38 pages, 24 figures, Minor Corrections, to appear in Phys.
Rev.
Magnetic Braking in Differentially Rotating, Relativistic Stars
We study the magnetic braking and viscous damping of differential rotation in
incompressible, uniform density stars in general relativity. Differentially
rotating stars can support significantly more mass in equilibrium than
nonrotating or uniformly rotating stars. The remnant of a binary neutron star
merger or supernova core collapse may produce such a "hypermassive" neutron
star. Although a hypermassive neutron star may be stable on a dynamical
timescale, magnetic braking and viscous damping of differential rotation will
ultimately alter the equilibrium structure, possibly leading to delayed
catastrophic collapse. Here we consider the slow-rotation, weak-magnetic field
limit in which E_rot << E_mag << W, where E_rot is the rotational kinetic
energy, E_mag is the magnetic energy, and W is the gravitational binding energy
of the star. We assume the system to be axisymmetric and solve the MHD
equations in both Newtonian gravitation and general relativity. Toroidal
magnetic fields are generated whenever the angular velocity varies along the
initial poloidal field lines. We find that the toroidal fields and angular
velocities oscillate independently along each poloidal field line, which
enables us to transform the original 2+1 equations into 1+1 form and solve them
along each field line independently. The incoherent oscillations on different
field lines stir up turbulent-like motion in tens of Alfven timescales ("phase
mixing"). In the presence of viscosity, the stars eventually are driven to
uniform rotation, with the energy contained in the initial differential
rotation going into heat. Our evolution calculations serve as qualitative
guides and benchmarks for future, more realistic MHD simulations in full 3+1
general relativity.Comment: 26 pages, 27 graphs, 1 table, accepted for publication by Phys. Rev.