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 $\mu$ 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 $\Psi_4$ 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 $w$ 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 $w$ 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 $w$ 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 $\psi_4$ and $\psi_0$, 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 $\Psi$ in outgoing or ingoing {\it radiation gauges}. In this paper we relate these potentials to what one actually computes in perturbation theory, i.e $\psi_4$ and $\psi_0$. 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 $\partial_t \Psi$ 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