80 research outputs found
Gravitational waveforms from a point particle orbiting a Schwarzschild black hole
We numerically solve the inhomogeneous Zerilli-Moncrief and Regge-Wheeler
equations in the time domain. We obtain the gravitational waveforms produced by
a point-particle of mass traveling around a Schwarzschild black hole of
mass M on arbitrary bound and unbound orbits. Fluxes of energy and angular
momentum at infinity and the event horizon are also calculated. Results for
circular orbits, selected cases of eccentric orbits, and parabolic orbits are
presented. The numerical results from the time-domain code indicate that, for
all three types of orbital motion, black hole absorption contributes less than
1% of the total flux, so long as the orbital radius r_p(t) satisfies r_p(t)> 5M
at all times.Comment: revtex4, 24 pages, 23 figures, 3 tables, submitted to PR
Isothermal Plasma Wave Properties of the Schwarzschild de-Sitter Black Hole in a Veselago Medium
In this paper, we study wave properties of isothermal plasma for the
Schwarzschild de-Sitter black hole in a Veselago medium. We use ADM 3+1
formalism to formulate general relativistic magnetohydrodynamical (GRMHD)
equations for the Schwarzschild de-Sitter spacetime in Rindler coordinates.
Further, Fourier analysis of the linearly perturbed GRMHD equations for the
rotating (non-magnetized and magnetized) background is taken whose determinant
leads to a dispersion relation. We investigate wave properties by using
graphical representation of the wave vector, the refractive index, change in
refractive index, phase and group velocities. Also, the modes of wave
dispersion are explored. The results indicate the existence of the Veselago
medium.Comment: 24 pages, 12 figures, accepted for publication in Astrophys. Space
Sci. arXiv admin note: text overlap with arXiv:1101.0884 and arxiv:1007.285
Dipole Perturbations of the Reissner-Nordstrom Solution: The Polar Case
The formalism developed by Chandrasekhar for the linear polar perturbations
of the Reissner-Nordstrom solution is generalized to include the case of dipole
(l=1) perturbations. Then, the perturbed metric coefficients and components of
the Maxwell tensor are computed.Comment: 16 pages, LaTeX, no figures. Submitted for publication in Physical
Review
A gravitational memory effect in "boosted" black hole perturbation theory
Black hole perturbation theory, or more generally, perturbation theory on a
Schwarzschild bockground, has been applied in several contexts, but usually
under the simplifying assumption that the ADM momentum vanishes, namely, that
the evolution is carried out and observed in the ``center of momentum frame''.
In this paper we consider some consequences of the inclusion of a non vanishing
ADM momentum in the initial data. We first provide a justification for the
validity of the transformation of the initial data to the ``center of momentum
frame'', and then analyze the effect of this transformation on the
gravitational wave amplitude. The most significant result is the possibility of
a type of gravitational memory effect that appears to have no simple relation
with the well known Christodoulou effect.Comment: REVTexIV, 15 pages, 2 EPS figure
Signatures of the sources in the gravitational waves of a perturbed Schwarzschild black hole
The explicit form of perturbation equation for the Weyl scalar,
containing the matter source terms, is derived for general type D spacetimes.
It is described in detail the particular case of the Schwarzschild spacetime
using in-going penetrating coordinates. As a practical application, we focused
on the emission of gravitational waves when a black hole is perturbed by a
surrounding dust-like fluid matter. The symmetries of the spacetime and the
simplicity of the matter source allow, by means of a spherical harmonic
decomposition, to study the problem by means of a one dimensional numerical
code.Comment: 17 pages, 8 figure
Perturbative evolution of conformally flat initial data for a single boosted black hole
The conformally flat families of initial data typically used in numerical
relativity to represent boosted black holes are not those of a boosted slice of
the Schwarzschild spacetime. If such data are used for each black hole in a
collision, the emitted radiation will be partially due to the ``relaxation'' of
the individual holes to ``boosted Schwarzschild'' form. We attempt to compute
this radiation by treating the geometry for a single boosted conformally flat
hole as a perturbation of a Schwarzschild black hole, which requires the use of
second order perturbation theory. In this we attempt to mimic a previous
calculation we did for the conformally flat initial data for spinning holes. We
find that the boosted black hole case presents additional subtleties, and
although one can evolve perturbatively and compute radiated energies, it is
much less clear than in the spinning case how useful for the study of
collisions are the radiation estimates for the ``spurious energy'' in each
hole. In addition to this we draw some lessons on which frame of reference
appears as more favorable for computing black hole collisions in the close
limit approximation.Comment: 11 pages, RevTex, 4 figures included with psfig, to appear in PR
The collision of two slowly rotating, initially non boosted, black holes in the close limit
We study the collision of two slowly rotating, initially non boosted, black
holes in the close limit. A ``punctures'' modification of the Bowen - York
method is used to construct conformally flat initial data appropriate to the
problem. We keep only the lowest nontrivial orders capable of giving rise to
radiation of both gravitational energy and angular momentum. We show that even
with these simplifications an extension to higher orders of the linear
Regge-Wheeler-Zerilli black hole perturbation theory, is required to deal with
the evolution equations of the leading contributing multipoles. This extension
is derived, together with appropriate extensions of the Regge-Wheeler and
Zerilli equations. The data is numerically evolved using these equations, to
obtain the asymptotic gravitational wave forms and amplitudes. Expressions for
the radiated gravitational energy and angular momentum are derived and used
together with the results of the numerical evolution to provide quantitative
expressions for the relative contribution of different terms, and their
significance is analyzed.Comment: revtex, 18 pages, 2 figures. Misprints corrected. To be published in
Phys. Rev.
Excitation of the odd-parity quasi-normal modes of compact objects
The gravitational radiation generated by a particle in a close unbounded
orbit around a neutron star is computed as a means to study the importance of
the modes of the neutron star. For simplicity, attention is restricted to
odd parity (``axial'') modes which do not couple to the neutron star's fluid
modes. We find that for realistic neutron star models, particles in unbounded
orbits only weakly excite the modes; we conjecture that this is also the
case for astrophysically interesting sources of neutron star perturbations. We
also find that for cases in which there is significant excitation of quadrupole
modes, there is comparable excitation of higher multipole modes.Comment: 18 pages, 21 figures, submitted to Phys. Rev.
Reconstruction of Black Hole Metric Perturbations from Weyl Curvature
Perturbation theory of rotating black holes is usually described in terms of
Weyl scalars and , which each satisfy Teukolsky's complex
master wave equation and respectively represent outgoing and ingoing radiation.
On the other hand metric perturbations of a Kerr hole can be described in terms
of (Hertz-like) potentials in outgoing or ingoing {\it radiation
gauges}. In this paper we relate these potentials to what one actually computes
in perturbation theory, i.e and . We explicitly construct
these relations in the nonrotating limit, preparatory to devising a
corresponding approach for building up the perturbed spacetime of a rotating
black hole. We discuss the application of our procedure to second order
perturbation theory and to the study of radiation reaction effects for a
particle orbiting a massive black hole.Comment: 6 Pages, Revtex
The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case
Gravitational perturbations about a Kerr black hole in the Newman-Penrose
formalism are concisely described by the Teukolsky equation. New numerical
methods for studying the evolution of such perturbations require not only the
construction of appropriate initial data to describe the collision of two
orbiting black holes, but also to know how such new data must be imposed into
the Teukolsky equation. In this paper we show how Cauchy data can be
incorporated explicitly into the Teukolsky equation for non-rotating black
holes. The Teukolsky function and its first time derivative
can be written in terms of only the 3-geometry and the
extrinsic curvature in a gauge invariant way. Taking a Laplace transform of the
Teukolsky equation incorporates initial data as a source term. We show that for
astrophysical data the straightforward Green function method leads to divergent
integrals that can be regularized like for the case of a source generated by a
particle coming from infinity.Comment: 9 pages, REVTEX. Misprints corrected in formulas (2.4)-(2.7). Final
version to appear in PR
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