On the instability of Reissner-Nordstrom black holes in de Sitter backgrounds

Recent numerical investigations have uncovered a surprising result: Reissner-Nordstrom-de Sitter black holes are unstable for spacetime dimensions larger than 6. Here we prove the existence of such instability analytically, and we compute the timescale in the near-extremal limit. We find very good agreement with the previous numerical results. Our results may me helpful in shedding some light on the nature of the instability.Comment: Published in Phys.Rev.

Perturbations of Schwarzschild black holes in Dynamical Chern-Simons modified gravity

Dynamical Chern-Simons (DCS) modified gravity is an attractive, yet relatively unexplored, candidate to an alternative theory of gravity. The DCS correction couples a dynamical scalar field to the gravitational field. In this framework, we analyze the perturbation formalism and stability properties of spherically symmetric black holes. Assuming that no background scalar field is present, gravitational perturbations with polar and axial parities decouple. We find no effect of the Chern-Simons coupling on the polar sector, while axial perturbations couple to the Chern-Simons scalar field. The axial sector can develop strong instabilities if the coupling parameter beta, associated to the dynamical coupling of the scalar field, is small enough; this yields a constraint on beta which is much stronger than the constraints previously known in the literature.Comment: 9 pages, 1 figure. Minor changes to match version accepted by Phys. Rev.

On the gravitational stability of D1-D5-P black holes

We examine the stability of the nonextremal D1-D5-P black hole solutions. In particular, we look for the appearance of a superradiant instability for the spinning black holes but we find no evidence of such an instability. We compare this situation with that for the smooth soliton geometries, which were recently observed to suffer from an ergoregion instability, and consider the implications for the fuzzball proposal.Comment: 18 pages, 3 figures. Minor comments added to match published versio

Visco-elastic regularization and strain softening

In this paper it is intended to verify the capacity of regularization of the numerical solution of an elasto-plastic problem with linear strain softening. The finite element method with a displacement approach is used. Drucker-Prager yield criteria is considered. The radial return method is used for the integration of the elasto-plastic constitutive relations. An elastovisco- plastic scheme is used to regularize the numerical solution. Two constitutive laws have been developed and implemented in a FE-program, the first represent the radial return method applied to Drucker-Prager yield criteria and the second is a time integration procedure for the Maxwell visco-elastic model. Attention is paid to finite deformations. An associative plastic flow is considered in the Drucker-Prager elasto-plastic model. The algorithms are tested in two problems with softening. Figures showing the capability of the algorithms to regularize the solution are presented

Late-Time Tails of Wave Propagation in Higher Dimensional Spacetimes

We study the late-time tails appearing in the propagation of massless fields (scalar, electromagnetic and gravitational) in the vicinities of a D-dimensional Schwarzschild black hole. We find that at late times the fields always exhibit a power-law falloff, but the power-law is highly sensitive to the dimensionality of the spacetime. Accordingly, for odd D>3 we find that the field behaves as t^[-(2l+D-2)] at late times, where l is the angular index determining the angular dependence of the field. This behavior is entirely due to D being odd, it does not depend on the presence of a black hole in the spacetime. Indeed this tails is already present in the flat space Green's function. On the other hand, for even D>4 the field decays as t^[-(2l+3D-8)], and this time there is no contribution from the flat background. This power-law is entirely due to the presence of the black hole. The D=4 case is special and exhibits, as is well known, the t^[-(2l+3)] behavior. In the extra dimensional scenario for our Universe, our results are strictly correct if the extra dimensions are infinite, but also give a good description of the late time behaviour of any field if the large extra dimensions are large enough.Comment: 6 pages, 3 figures, RevTeX4. Version to appear in Rapid Communications of Physical Review

Testing strong gravity with gravitational waves and Love numbers

The LIGO observation of GW150914 has inaugurated the gravitational-wave astronomy era and the possibility of testing gravity in extreme regimes. While distorted black holes are the most convincing sources of gravitational waves, similar signals might be produced also by other compact objects. In particular, we discuss what the gravitational-wave ringdown could tell us about the nature of the emitting object, and how measurements of the tidal Love numbers could help us in understanding the internal structure of compact dark objects

Numerical analysis of quasinormal modes in nearly extremal Schwarzschild-de Sitter spacetimes

We calculate high-order quasinormal modes with large imaginary frequencies for electromagnetic and gravitational perturbations in nearly extremal Schwarzschild-de Sitter spacetimes. Our results show that for low-order quasinormal modes, the analytical approximation formula in the extremal limit derived by Cardoso and Lemos is a quite good approximation for the quasinormal frequencies as long as the model parameter $r_1\kappa_1$ is small enough, where $r_1$ and $\kappa_1$ are the black hole horizon radius and the surface gravity, respectively. For high-order quasinormal modes, to which corresponds quasinormal frequencies with large imaginary parts, on the other hand, this formula becomes inaccurate even for small values of $r_1\kappa_1$. We also find that the real parts of the quasinormal frequencies have oscillating behaviors in the limit of highly damped modes, which are similar to those observed in the case of a Reissner-Nordstr{\" o}m black hole. The amplitude of oscillating ${\rm Re(\omega)}$ as a function of ${\rm Im}(\omega)$ approaches a non-zero constant value for gravitational perturbations and zero for electromagnetic perturbations in the limit of highly damped modes, where $\omega$ denotes the quasinormal frequency. This means that for gravitational perturbations, the real part of quasinormal modes of the nearly extremal Schwarzschild-de Sitter spacetime appears not to approach any constant value in the limit of highly damped modes. On the other hand, for electromagnetic perturbations, the real part of frequency seems to go to zero in the limit.Comment: 9 pages, 7 figures, to appear in Physical Review

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

Quasinormal modes for the SdS black hole : an analytical approximation scheme

Quasinormal modes for scalar field perturbations of a Schwarzschild-de Sitter (SdS) black hole are investigated. An analytical approximation is proposed for the problem. The quasinormal modes are evaluated for this approximate model in the limit when black hole mass is much smaller than the radius of curvature of the spacetime. The model mirrors some striking features observed in numerical studies of time behaviour of scalar perturbations of the SdS black hole. In particular, it shows the presence of two sets of modes relevant at two different time scales, proportional to the surface gravities of the black hole and cosmological horizons respectively. These quasinormal modes are not complete - another feature observed in numerical studies. Refinements of this model to yield more accurate quantitative agreement with numerical studies are discussed. Further investigations of this model are outlined, which would provide a valuable insight into time behaviour of perturbations in the SdS spacetime.Comment: 12 pages, revtex, refs added and discussion expanded, version to appear in Phys. Rev.