La nuova Anuac: editoriale

Editorial article from the new Editor-in-Chief

Perturbations and Stability of Black Ellipsoids

We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of diagonal metrics. The analysis is performed in the approximation of small eccentricity deformations of the Schwarzschild solution. We conclude that such anisotropic black hole objects may be stable with respect to the perturbations parametrized by the Schrodinger equations in the framework of the one--dimensional inverse scattering theory.Comment: Published variant in IJMD with small modifications in formulas and new reference

Electromagnetic radiation from collisions at almost the speed of light: an extremely relativistic charged particle falling into a Schwarzschild black hole

We investigate the electromagnetic radiation released during the high energy collision of a charged point particle with a four-dimensional Schwarzschild black hole. We show that the spectra is flat, and well described by a classical calculation. We also compare the total electromagnetic and gravitational energies emitted, and find that the former is supressed in relation to the latter for very high energies. These results could apply to the astrophysical world in the case charged stars and small charged black holes are out there colliding into large black holes, and to a very high energy collision experiment in a four-dimensional world. In this latter scenario the calculation is to be used for the moments just after the black hole formation, when the collision of charged debris with the newly formed black hole is certainly expected. Since the calculation is four-dimensional, it does not directly apply to Tev-scale gravity black holes, as these inhabit a world of six to eleven dimensions, although our results should qualitatively hold when extrapolated with some care to higher dimensions.Comment: 6 pages, 2 figure

Cold Plasma Dispersion Relations in the Vicinity of a Schwarzschild Black Hole Horizon

We apply the ADM 3+1 formalism to derive the general relativistic magnetohydrodynamic equations for cold plasma in spatially flat Schwarzschild metric. Respective perturbed equations are linearized for non-magnetized and magnetized plasmas both in non-rotating and rotating backgrounds. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed for the existence of waves with positive angular frequency in the region near the horizon. Our results support the fact that no information can be extracted from the Schwarzschild black hole. It is concluded that negative phase velocity propagates in the rotating background whether the black hole is rotating or non-rotating.Comment: 27 pages, 11 figures accepted for publication in Gen. Relat. & Gravi

Understanding initial data for black hole collisions

Numerical relativity, applied to collisions of black holes, starts with initial data for black holes already in each other's strong field. The initial hypersurface data typically used for computation is based on mathematical simplifying prescriptions, such as conformal flatness of the 3-geometry and longitudinality of the extrinsic curvature. In the case of head on collisions of equal mass holes, there is evidence that such prescriptions work reasonably well, but it is not clear why, or whether this success is more generally valid. Here we study these questions by considering the ``particle limit'' for head on collisions of nonspinning holes. Einstein's equations are linearized in the mass of the small hole, and described by a single gauge invariant spacetime function psi, for each multipole. The resulting equations have been solved by numerical evolution for collisions starting from various initial separations, and the evolution is studied on a sequence of hypersurfaces. In particular, we extract hypersurface data, that is psi and its time derivative, on surfaces of constant background Schwarzschild time. These evolved data can then be compared with ``prescribed'' data, evolved data can be replaced by prescribed data on any hypersurface, and evolved further forward in time, a gauge invariant measure of deviation from conformal flatness can be evaluated, etc. The main findings of this study are: (i) For holes of unequal mass the use of prescribed data on late hypersurfaces is not successful. (ii) The failure is likely due to the inability of the prescribed data to represent the near field of the smaller hole. (iii) The discrepancy in the extrinsic curvature is more important than in the 3-geometry. (iv) The use of the more general conformally flat longitudinal data does not notably improve this picture.Comment: 20 pages, REVTEX, 26 PS figures include

Colliding Black Holes: The Close Limit

The problem of the mutual attraction and joining of two black holes is of importance as both a source of gravitational waves and as a testbed of numerical relativity. If the holes start out close enough that they are initially surrounded by a common horizon, the problem can be viewed as a perturbation of a single black hole. We take initial data due to Misner for close black holes, apply perturbation theory and evolve the data with the Zerilli equation. The computed gravitational radiation agrees with and extends the results of full numerical computations.Comment: 4 pages, Revtex, 3 postscript figures included, CGPG-94/2-

Head-on collisions of black holes: the particle limit

We compute gravitational radiation waveforms, spectra and energies for a point particle of mass $m_0$ falling from rest at radius $r_0$ into a Schwarzschild hole of mass $M$. This radiation is found to lowest order in $(m_0/M)$ with the use of a Laplace transform. In contrast with numerical relativity results for head-on collisions of equal-mass holes, the radiated energy is found not to be a monotonically increasing function of initial separation; there is a local radiated-energy maximum at $r_0\approx4.5M$. The present results, along with results for infall from infinity, provide a complete catalog of waveforms and spectra for particle infall. We give a representative sample from that catalog and an interesting observation: Unlike the simple spectra for other head-on collisions (either of particle and hole, or of equal mass holes) the spectra for $\infty>r_0>\sim5M$ show a series of evenly spaced bumps. A simple explanation is given for this. Lastly, our energy vs. $r_0$ results are compared with approximation methods used elsewhere, for small and for large initial separation.Comment: 15 pages, REVTeX, 25 figure

Evolving the Bowen-York initial data for spinning black holes

The Bowen-York initial value data typically used in numerical relativity to represent spinning black hole are not those of a constant-time slice of the Kerr spacetime. If Bowen-York initial 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 Kerr form. We compute this radiation by treating the geometry for a single hole as a perturbation of a Schwarzschild black hole, and by using second order perturbation theory. We discuss the extent to which Bowen-York data can be expected accurately to represent Kerr holes.Comment: 10 pages, RevTeX, 4 figures included with psfi

Electromagnetic waves around dilatonic stars and naked singularities

We study the propagation of classical electromagnetic waves on the simplest four-dimensional spherically symmetric metric with a dilaton background field. Solutions to the relevant equations are obtained perturbatively in a parameter which measures the strength of the dilaton field (hence parameterizes the departure from Schwarzschild geometry). The loss of energy from outgoing modes is estimated as a back-scattering process against the dilaton background, which would affect the luminosity of stars with a dilaton field. The radiation emitted by a freely falling point-like source on such a background is also studied by analytical and numerical methods.Comment: 9 pages, 1 figur

Shell sources as a probe of relativistic effects in neutron star models

A perturbing shell is introduced as a device for studying the excitation of fluid motions in relativistic stellar models. We show that this approach allows a reasonably clean separation of radiation from the shell and from fluid motions in the star, and provides broad flexibility in the location and timescale of perturbations driving the fluid motions. With this model we compare the relativistic and Newtonian results for the generation of even parity gravitational waves from constant density models. Our results suggest that relativistic effects will not be important in computations of the gravitational emission except possibly in the case of excitation of the neutron star on very short time scales.Comment: 16 pages LaTeX with 6 eps figures; submitted to Phys. Rev.