55 research outputs found
Parametric amplification of waves during gravitational collapse: a first investigation
We study the dynamical evolution of perturbations in the gravitational field
of a collapsing fluid star. Specifically, we consider the initial value problem
for a massless scalar field in a spacetime similar to the Oppenheimer-Snyder
collapse model, and numerically evolve in time the relevant wave equation. Our
main objective is to examine whether the phenomenon of parametric
amplification, known to be responsible for the strong amplification of
primordial perturbations in the expanding Universe, can efficiently operate
during gravitational collapse. Although the time-varying gravitational field
inside the star can, in principle, support such a process, we nevertheless find
that the perturbing field escapes from the star too early for amplification to
become significant. To put an upper limit in the efficiency of the
amplification mechanism (for a scalar field) we furthermore consider the case
of perturbations trapped inside the star for the entire duration of the
collapse. In this extreme case, the field energy is typically amplified at the
level ~ 1% when the star is about to cross its Schwarszchild radius.
Significant amplification is observed at later stages when the star has even
smaller radius. Therefore, the conclusion emerging from our simple model is
that parametric amplification is unlikely to be of significance during
gravitational collapse. Further work, based on more realistic collapse models,
is required in order to fully assess the astrophysical importance of parametric
amplification.Comment: 14 pages, revtex, 9 eps figure
On the orbital and physical parameters of the HDE 226868/Cygnus X-1 binary system
In this paper we explore the consequences of the recent determination of the
mass m=(8.7 +/- 0.8)M_Sun of Cygnus X-1, obtained from the Quasi-Periodic
Oscillation (QPO)-photon index correlation scaling, on the orbital and physical
properties of the binary system HDE 226868/Cygnus X-1. By using such a result
and the latest spectroscopic optical data of the HDE 226868 supergiant star we
get M=(24 +/- 5)M_Sun for its mass. It turns out that deviations from the third
Kepler law significant at more than 1-sigma level would occur if the
inclination i of the system's orbital plane to the plane of the sky falls
outside the range 41-56 deg: such deviations cannot be due to the first
post-Newtonian (1PN) correction to the orbital period because of its smallness;
interpreted in the framework of the Newtonian theory of gravitation as due to
the stellar quadrupole mass moment Q, they are unphysical because Q would take
unreasonably large values. By conservatively assuming that the third Kepler law
is an adequate model for the orbital period we obtain i=(48 +/- 7) deg which
yields for the relative semimajor axis a=(42 +/- 9)R_Sun. Our estimate for the
Roche's lobe of HDE 226868 is r_M = (21 +/- 6)R_Sun.Comment: Latex2e, 7 pages, 1 table, 4 figures. To appear in ApSS (Astrophysics
and Space Science
An inverse approach to Einstein's equations for non-conducting fluids
We show that a flow (timelike congruence) in any type warped product
spacetime is uniquely and algorithmically determined by the condition of zero
flux. (Though restricted, these spaces include many cases of interest.) The
flow is written out explicitly for canonical representations of the spacetimes.
With the flow determined, we explore an inverse approach to Einstein's
equations where a phenomenological fluid interpretation of a spacetime follows
directly from the metric irrespective of the choice of coordinates. This
approach is pursued for fluids with anisotropic pressure and shear viscosity.
In certain degenerate cases this interpretation is shown to be generically not
unique. The framework developed allows the study of exact solutions in any
frame without transformations. We provide a number of examples, in various
coordinates, including spacetimes with and without unique interpretations. The
results and algorithmic procedure developed are implemented as a computer
algebra program called GRSource.Comment: 9 pages revtex4. Final form to appear in Phys Rev
Motion and gravitational wave forms of eccentric compact binaries with orbital-angular-momentum-aligned spins under next-to-leading order in spin-orbit and leading order in spin(1)-spin(2) and spin-squared couplings
A quasi-Keplerian parameterisation for the solutions of second post-Newtonian
(PN) accurate equations of motion for spinning compact binaries is obtained
including leading order spin-spin and next-to-leading order spin-orbit
interactions. Rotational deformation of the compact objects is incorporated.
For arbitrary mass ratios the spin orientations are taken to be parallel or
anti-parallel to the orbital angular momentum vector. The emitted gravitational
wave forms are given in analytic form up to 2PN point particle, 1.5PN spin
orbit and 1PN spin-spin contributions, where the spins are counted of 0PN
order.Comment: 26 pages, 1 figure, published in CQG. Current version: we removed a
remark and clarified the derivation of the orbital element \e_ph
Radiative falloff in Einstein-Straus spacetime
The Einstein-Straus spacetime describes a nonrotating black hole immersed in
a matter-dominated cosmology. It is constructed by scooping out a spherical
ball of the dust and replacing it with a vacuum region containing a black hole
of the same mass. The metric is smooth at the boundary, which is comoving with
the rest of the universe. We study the evolution of a massless scalar field in
the Einstein-Straus spacetime, with a special emphasis on its late-time
behavior. This is done by numerically integrating the scalar wave equation in a
double-null coordinate system that covers both portions (vacuum and dust) of
the spacetime. We show that the field's evolution is governed mostly by the
strong concentration of curvature near the black hole, and the discontinuity in
the dust's mass density at the boundary; these give rise to a rather complex
behavior at late times. Contrary to what it would do in an asymptotically-flat
spacetime, the field does not decay in time according to an inverse power-law.Comment: ReVTeX, 12 pages, 14 figure
Scalar wave propagation in topological black hole backgrounds
We consider the evolution of a scalar field coupled to curvature in
topological black hole spacetimes. We solve numerically the scalar wave
equation with different curvature-coupling constant and show that a rich
spectrum of wave propagation is revealed when is introduced. Relations
between quasinormal modes and the size of different topological black holes
have also been investigated.Comment: 26 pages, 18 figure
Radiative falloff in Schwarzschild-de Sitter spacetime
We consider the time evolution of a scalar field propagating in
Schwarzschild-de Sitter spacetime. At early times, the field behaves as if it
were in pure Schwarzschild spacetime; the structure of spacetime far from the
black hole has no influence on the evolution. In this early epoch, the field's
initial outburst is followed by quasi-normal oscillations, and then by an
inverse power-law decay. At intermediate times, the power-law behavior gives
way to a faster, exponential decay. At late times, the field behaves as if it
were in pure de Sitter spacetime; the structure of spacetime near the black
hole no longer influences the evolution in a significant way. In this late
epoch, the field's behavior depends on the value of the curvature-coupling
constant xi. If xi is less than a critical value 3/16, the field decays
exponentially, with a decay constant that increases with increasing xi. If xi >
3/16, the field oscillates with a frequency that increases with increasing xi;
the amplitude of the field still decays exponentially, but the decay constant
is independent of xi.Comment: 10 pages, ReVTeX, 5 figures, references updated, and new section
adde
Radiative falloff of a scalar field in a weakly curved spacetime without symmetries
We consider a massless scalar field propagating in a weakly curved spacetime
whose metric is a solution to the linearized Einstein field equations. The
spacetime is assumed to be stationary and asymptotically flat, but no other
symmetries are imposed -- the spacetime can rotate and deviate strongly from
spherical symmetry. We prove that the late-time behavior of the scalar field is
identical to what it would be in a spherically-symmetric spacetime: it decays
in time according to an inverse power-law, with a power determined by the
angular profile of the initial wave packet (Price falloff theorem). The field's
late-time dynamics is insensitive to the nonspherical aspects of the metric,
and it is governed entirely by the spacetime's total gravitational mass; other
multipole moments, and in particular the spacetime's total angular momentum, do
not enter in the description of the field's late-time behavior. This extended
formulation of Price's falloff theorem appears to be at odds with previous
studies of radiative decay in the spacetime of a Kerr black hole. We show,
however, that the contradiction is only apparent, and that it is largely an
artifact of the Boyer-Lindquist coordinates adopted in these studies.Comment: 17 pages, RevTeX
Exact Solution for the Exterior Field of a Rotating Neutron Star
A four-parameter class of exact asymptotically flat solutions of the
Einstein-Maxwell equations involving only rational functions is presented. It
is able to describe the exterior field of a slowly or rapidly rotating neutron
star with poloidal magnetic field.Comment: Accepted for publication in Phys. Rev. D as Rapid Communication. 8
pages, 2 eps figure
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