The collision of boosted black holes: second order close limit calculations

We study the head-on collision of black holes starting from unsymmetrized, Brill--Lindquist type data for black holes with non-vanishing initial linear momentum. Evolution of the initial data is carried out with the ``close limit approximation,'' in which small initial separation and momentum are assumed, and second-order perturbation theory is used. We find agreement that is remarkably good, and that in some ways improves with increasing momentum. This work extends a previous study in which second order perturbation calculations were used for momentarily stationary initial data, and another study in which linearized perturbation theory was used for initially moving holes. In addition to supplying answers about the collisions, the present work has revealed several subtle points about the use of higher order perturbation theory, points that did not arise in the previous studies. These points include issues of normalization, and of comparison with numerical simulations, and will be important to subsequent applications of approximation methods for collisions.Comment: 20 pages, RevTeX, 6 figures included with psfi

The initial value problem for linearized gravitational perturbations of the Schwarzschild naked singularity

The coupled equations for the scalar modes of the linearized Einstein equations around Schwarzschild's spacetime were reduced by Zerilli to a 1+1 wave equation with a potential $V$, on a field $\Psi_z$. For smooth metric perturbations $\Psi_z$ is singular at $r_s=-6M/(\ell-1)(\ell+2)$, $\ell$ the mode harmonic number, and $V$ has a second order pole at $r_s$. This is irrelevant to the black hole exterior stability problem, where $r>2M>0$, and $r_s <0$, but it introduces a non trivial problem in the naked singular case where $M0$, and the singularity appears in the relevant range of $r$. We solve this problem by developing a new approach to the evolution of the even mode, based on a {\em new gauge invariant function}, $\hat \Psi$ -related to $\Psi_z$ by an intertwiner operator- that is a regular function of the metric perturbation {\em for any value of $M$}. This allows to address the issue of evolution of gravitational perturbations in this non globally hyperbolic background, and to complete the proof of the linear instability of the Schwarzschild naked singularity, by showing that a previously found unstable mode is excitable by generic initial data. This is further illustrated by numerically solving the linearized equations for suitably chosen initial data.Comment: typos corrected, references adde

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

Nonequilibrium Precursor Model for the Onset of Percolation in a Two-Phase System

Using a Boltzmann equation, we investigate the nonequilibrium dynamics of nonperturbative fluctuations within the context of Ginzburg-Landau models. As an illustration, we examine how a two-phase system initially prepared in a homogeneous, low-temperature phase becomes populated by precursors of the opposite phase as the temperature is increased. We compute the critical value of the order parameter for the onset of percolation, which signals the breakdown of the conventional dilute gas approximation.Comment: 4 pages, 4 eps figures (uses epsf), Revtex. Replaced with version in press Physical Review

On low energy quantum gravity induced effects on the propagation of light

Present models describing the interaction of quantum Maxwell and gravitational fields predict a breakdown of Lorentz invariance and a non standard dispersion relation in the semiclassical approximation. Comparison with observational data however, does not support their predictions. In this work we introduce a different set of ab initio assumptions in the canonical approach, namely that the homogeneous Maxwell equations are valid in the semiclassical approximation, and find that the resulting field equations are Lorentz invariant in the semiclassical limit. We also include a phenomenological analysis of possible effects on the propagation of light, and their dependence on energy, in a cosmological context.Comment: 12 page

Linear stability of Einstein-Gauss-Bonnet static spacetimes. Part II: vector and scalar perturbations

We study the stability under linear perturbations of a class of static solutions of Einstein-Gauss-Bonnet gravity in $D=n+2$ dimensions with spatial slices of the form \Sigma_{\k}^n \times {\mathbb R}^+, \Sigma_{\k}^n an $n-$manifold of constant curvature \k. Linear perturbations for this class of space-times can be generally classified into tensor, vector and scalar types. In a previous paper, tensor perturbations were analyzed. In this paper we study vector and scalar perturbations. We show that vector perturbations can be analyzed in general using an S-deformation approach and do not introduce instabilities. On the other hand, we show by analyzing an explicit example that, contrary to what happens in Einstein gravity, scalar perturbations may lead to instabilities in black holes with spherical horizons when the Gauss-Bonnet string corrections are taken into account.Comment: 16 pages, 6 figure

Gravitational instabilities in Kerr space-times

In this paper we consider the possible existence of unstable axisymmetric modes in Kerr space times, resulting from exponentially growing solutions of the Teukolsky equation. We describe a transformation that casts the radial equation that results upon separation of variables in the Teukolsky equation, in the form of a Schr\"odinger equation, and combine the properties of the solutions of this equations with some recent results on the asymptotic behaviour of spin weighted spheroidal harmonics to prove the existence of an infinite family of unstable modes. Thus we prove that the stationary region beyond a Kerr black hole inner horizon is unstable under gravitational linear perturbations. We also prove that Kerr space-time with angular momentum larger than its square mass, which has a naked singularity, is unstable.Comment: 9 pages, 4 figures, comments, references and calculation details added, asymptotic expansion typos fixe

Drake Equation for the Multiverse: From the String Landscape to Complex Life

It is argued that selection criteria usually referred to as "anthropic conditions" for the existence of intelligent (typical) observers widely adopted in cosmology amount only to preconditions for primitive life. The existence of life does not imply in the existence of intelligent life. On the contrary, the transition from single-celled to complex, multi-cellular organisms is far from trivial, requiring stringent additional conditions on planetary platforms. An attempt is made to disentangle the necessary steps leading from a selection of universes out of a hypothetical multiverse to the existence of life and of complex life. It is suggested that what is currently called the "anthropic principle" should instead be named the "prebiotic principle."Comment: 6 pages, RevTeX, in press, Int. J. Mod. Phys.

Self-gravitating splitting thin shells

In this paper we show that thin shells in spherically symmetric spacetimes, whose matter content is described by a pair of non-interacting spherically symmetric matter fields, generically exhibit instability against an infinitesimal separation of its constituent fields. We give explicit examples and construct solutions that represent a shell that splits into two shells. Then we extend those results for 5-dimensional Schwarzschild-AdS bulk spacetimes, which is a typical scenario for brane-world models, and show that the same kind of stability analysis and splitting solution can be constructed. We find that a widely proposed family of brane-world models are extremely unstable in this sense. Finally, we discuss possible interpretations of these features and their relation to the initial value problem for concentrated sources.Comment: 18 pages, 3 figure

Soliton Solutions with Real Poles in the Alekseev formulation of the Inverse-Scattering method

A new approach to the inverse-scattering technique of Alekseev is presented which permits real-pole soliton solutions of the Ernst equations to be considered. This is achieved by adopting distinct real poles in the scattering matrix and its inverse. For the case in which the electromagnetic field vanishes, some explicit solutions are given using a Minkowski seed metric. The relation with the corresponding soliton solutions that can be constructed using the Belinskii-Zakharov inverse-scattering technique is determined.Comment: 8 pages, LaTe