Perturbative evolution of the static configurations, quasinormal modes and quasi normal ringing in the Apostolatos - Thorne cylindrical shell model

We study the perturbative evolution of the static configurations, quasinormal modes and quasi normal ringing in the Apostolatos - Thorne cylindrical shell model. We consider first an expansion in harmonic modes and show that it provides a complete solution for the characteristic value problem for the finite perturbations of a static configuration. As a consequence of this completeness we obtain a proof of the stability of static solutions under this type of perturbations. The explicit expression for the mode expansion are then used to obtain numerical values for some of the quasi normal mode complex frequencies. Some examples involving the numerical evaluation of the integral mode expansions are described and analyzed, and the quasi normal ringing displayed by the solutions is found to be in agreement with quasi normal modes found previously. Going back to the full relativistic equations of motion we find their general linear form by expanding to first order about a static solution. We then show that the resulting set of coupled ordinary and partial differential equations for the dynamical variables of the system can be used to set an initial plus boundary values problem, and prove that there is an associated positive definite constant of the motion that puts absolute bounds on the dynamic variables of the system, establishing the stability of the motion of the shell under arbitrary, finite perturbations. We also show that the problem can be solved numerically, and provide some explicit examples that display the complete agreement between the purely numerical evolution and that obtained using the mode expansion, in particular regarding the quasi normal ringing that results in the evolution of the system. We also discuss the relation of the present work to some recent results on the same model that have appeared in the literature.Comment: 27 pages, 7 figure

Self lensing effects for compact stars and their mass-radius relation

During the last couple of years astronomers and astrophysicists have been debating on the fact whether the so called `strange stars' - stars made up of strange quark matter, have been discovered with the candidates like SAX J1808.4-3658, 4U 1728-34, RX J1856.5-3754, etc. The main contention has been the estimation of radius of the star for an assumed mass of ~ 1.4 M_sun and to see whether the point overlaps with the graphs for the neutron star equation of state or whether it goes to the region of stars made of strange matter equation of state. Using the well established formulae from general relativity for the gravitational redshift and the `lensing effect' due to bending of photon trajectories, we, in this letter, relate the parameters M and R with the observable parameters, the redshift z and the radiation radius R_\infty, thus constraining both M and R for specific ranges, without any other arbitrariness. With the required inputs from observations, one ought to incorporate the effects of self lensing of the compact stars which has been otherwise ignored in all of the estimations done so far. Nonetheless, these effect of self lensing makes a marked difference and constraints on the M-R relation.Comment: 7 pages, 1 figure, accepted for publication in Mod. Phys. Lett.

Analytic structure of radiation boundary kernels for blackhole perturbations

Exact outer boundary conditions for gravitational perturbations of the Schwarzschild metric feature integral convolution between a time-domain boundary kernel and each radiative mode of the perturbation. For both axial (Regge-Wheeler) and polar (Zerilli) perturbations, we study the Laplace transform of such kernels as an analytic function of (dimensionless) Laplace frequency. We present numerical evidence indicating that each such frequency-domain boundary kernel admits a "sum-of-poles" representation. Our work has been inspired by Alpert, Greengard, and Hagstrom's analysis of nonreflecting boundary conditions for the ordinary scalar wave equation.Comment: revtex4, 14 pages, 12 figures, 3 table

Quasinormal Modes, the Area Spectrum, and Black Hole Entropy

The results of canonical quantum gravity concerning geometric operators and black hole entropy are beset by an ambiguity labelled by the Immirzi parameter. We use a result from classical gravity concerning the quasinormal mode spectrum of a black hole to fix this parameter in a new way. As a result we arrive at the Bekenstein - Hawking expression of $A/4 l_P^2$ for the entropy of a black hole and in addition see an indication that the appropriate gauge group of quantum gravity is SO(3) and not its covering group SU(2).Comment: 4 pages, 2 figure

Kerr black hole quasinormal frequencies

Black-hole quasinormal modes (QNM) have been the subject of much recent attention, with the hope that these oscillation frequencies may shed some light on the elusive theory of quantum gravity. We compare numerical results for the QNM spectrum of the (rotating) Kerr black hole with an {\it exact} formula Re$\omega \to T_{BH}\ln 3+\Omega m$, which is based on Bohr's correspondence principle. We find a close agreement between the two. Possible implications of this result to the area spectrum of quantum black holes are discussed.Comment: 3 pages, 2 figure

Extreme gravitational lensing in vicinity of Schwarzschild-de Sitter black holes

We have developed a realistic, fully general relativistic computer code to simulate optical projection in a strong, spherically symmetric gravitational field. The standard theoretical analysis of optical projection for an observer in the vicinity of a Schwarzschild black hole is extended to black hole spacetimes with a repulsive cosmological constant, i.e, Schwarzschild-de Sitter spacetimes. Influence of the cosmological constant is investigated for static observers and observers radially free-falling from the static radius. Simulations include effects of the gravitational lensing, multiple images, Doppler and gravitational frequency shift, as well as the intensity amplification. The code generates images of the sky for the static observer and a movie simulations of the changing sky for the radially free-falling observer. Techniques of parallel programming are applied to get a high performance and a fast run of the BHC simulation code

Comparison of area spectra in loop quantum gravity

We compare two area spectra proposed in loop quantum gravity in different approaches to compute the entropy of the Schwarzschild black hole. We describe the black hole in general microcanonical and canonical area ensembles for these spectra. We show that in the canonical ensemble, the results for all statistical quantities for any spectrum can be reproduced by a heuristic picture of Bekenstein up to second order. For one of these spectra - the equally-spaced spectrum - in light of a proposed connection of the black hole area spectrum to the quasinormal mode spectrum and following hep-th/0304135, we present explicit calculations to argue that this spectrum is completely consistent with this connection. This follows without requiring a change in the gauge group of the spin degrees of freedom in this formalism from SU(2) to SO(3). We also show that independent of the area spectrum, the degeneracy of the area observable is bounded by $C A\exp(A/4)$, where $A$ is measured in Planck units and $C$ is a constant of order unity.Comment: 8 pages, Revtex 4, version to appear in Classical and Quantum Gravit

Neutrino quasinormal modes of the Reissner-Nordstr\"om black hole

The neutrino quasinormal modes of the Reissner-Nordstr\"om (RN) black hole are investigated using continued fraction approach. We find, for large angular quantum number, that the quasinormal frequencies become evenly spaced and the spacing of the real part depends on the charge of the black hole and that of the imaginary part is zero. We then find that the quasinormal frequencies in the complex $\omega$ plane move counterclockwise as the charge increases. They get a spiral-like shape, moving out of their Schwarzschild value and ``looping in" towards some limiting frequency as the charge tends to the extremal value. The number of the spirals increases as the overtone number increases but it decreases as the angular quantum number increases. We also find that both the real and imaginary parts are oscillatory functions of the charge, and the oscillation becomes faster as the overtone number increases but it becomes slower as the angular quantum number increases.Comment: 11 pages, 3 figure

Quasi-normal modes of Schwarzschild-de Sitter black holes

The low-laying frequencies of characteristic quasi-normal modes (QNM) of Schwarzschild-de Sitter (SdS) black holes have been calculated for fields of different spin using the 6th-order WKB approximation and the approximation by the P\"{o}shl-Teller potential. The well-known asymptotic formula for large $l$ is generalized here on a case of the Schwarzchild-de Sitter black hole. In the limit of the near extreme $\Lambda$ term the results given by both methods are in a very good agreement, and in this limit fields of different spin decay with the same rate.Comment: 9 pages, 1 ancillary Mathematica(R) noteboo

Boundary conditions at spatial infinity for fields in Casimir calculations

The importance of imposing proper boundary conditions for fields at spatial infinity in the Casimir calculations is elucidated.Comment: 8 pages, 1 figure, submitted to the Proceedings of The Seventh Workshop QFEXT'05 (Barcelona, September 5-9, 2005