Co-accelerated particles in the C-metric

With appropriately chosen parameters, the C-metric represents two uniformly accelerated black holes moving in the opposite directions on the axis of the axial symmetry (the z-axis). The acceleration is caused by nodal singularities located on the z-axis. In the~present paper, geodesics in the~C-metric are examined. In general there exist three types of timelike or null geodesics in the C-metric: geodesics describing particles 1) falling under the black hole horizon; 2)crossing the acceleration horizon; and 3) orbiting around the z-axis and co-accelerating with the black holes. Using an effective potential, it can be shown that there exist stable timelike geodesics of the third type if the product of the parameters of the C-metric, mA, is smaller than a certain critical value. Null geodesics of the third type are always unstable. Special timelike and null geodesics of the third type are also found in an analytical form.Comment: 10 pages, 12 EPS figures, changes mainly in abstract & introductio

Chaotic Scattering and Capture of Strings by Black Hole

We consider scattering and capture of circular cosmic strings by a Schwarzschild black hole. Although being a priori a very simple axially symmetric two-body problem, it shows all the features of chaotic scattering. In particular, it contains a fractal set of unstable periodic solutions; a so-called strange repellor. We study the different types of trajectories and obtain the fractal dimension of the basin-boundary separating the space of initial conditions according to the different asymptotic outcomes. We also consider the fractal dimension as a function of energy, and discuss the transition from order to chaos.Comment: RevTeX 3.1, 9 pages, 5 figure

Boost-rotation symmetric type D radiative metrics in Bondi coordinates

The asymptotic properties of the solutions to the Einstein-Maxwell equations with boost-rotation symmetry and Petrov type D are studied. We find series solutions to the pertinent set of equations which are suitable for a late time descriptions in coordinates which are well adapted for the description of the radiative properties of spacetimes (Bondi coordinates). By calculating the total charge, Bondi and NUT mass and the Newman-Penrose constants of the spacetimes we provide a physical interpretation of the free parameters of the solutions. Additional relevant aspects on the asymptotics and radiative properties of the spacetimes considered, such as the possible polarization states of the gravitational and electromagnetic field, are discussed through the way

Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy

The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a gravitational wave signal. The analysis of data from ground based gravitational wave detectors is mostly conducted using classical statistics, and methods such as the Neyman-Pearson criteria are used for model selection. Future space based detectors, such as the \emph{Laser Interferometer Space Antenna} (LISA), are expected to produced rich data streams containing the signals from many millions of sources. Determining the number of sources that are resolvable, and the most appropriate description of each source poses a challenging model selection problem that may best be addressed in a Bayesian framework. An important class of LISA sources are the millions of low-mass binary systems within our own galaxy, tens of thousands of which will be detectable. Not only are the number of sources unknown, but so are the number of parameters required to model the waveforms. For example, a significant subset of the resolvable galactic binaries will exhibit orbital frequency evolution, while a smaller number will have measurable eccentricity. In the Bayesian approach to model selection one needs to compute the Bayes factor between competing models. Here we explore various methods for computing Bayes factors in the context of determining which galactic binaries have measurable frequency evolution. The methods explored include a Reverse Jump Markov Chain Monte Carlo (RJMCMC) algorithm, Savage-Dickie density ratios, the Schwarz-Bayes Information Criterion (BIC), and the Laplace approximation to the model evidence. We find good agreement between all of the approaches.Comment: 11 pages, 6 figure

Detection Strategies for Extreme Mass Ratio Inspirals

The capture of compact stellar remnants by galactic black holes provides a unique laboratory for exploring the near horizon geometry of the Kerr spacetime, or possible departures from general relativity if the central cores prove not to be black holes. The gravitational radiation produced by these Extreme Mass Ratio Inspirals (EMRIs) encodes a detailed map of the black hole geometry, and the detection and characterization of these signals is a major scientific goal for the LISA mission. The waveforms produced are very complex, and the signals need to be coherently tracked for hundreds to thousands of cycles to produce a detection, making EMRI signals one of the most challenging data analysis problems in all of gravitational wave astronomy. Estimates for the number of templates required to perform an exhaustive grid-based matched-filter search for these signals are astronomically large, and far out of reach of current computational resources. Here I describe an alternative approach that employs a hybrid between Genetic Algorithms and Markov Chain Monte Carlo techniques, along with several time saving techniques for computing the likelihood function. This approach has proven effective at the blind extraction of relatively weak EMRI signals from simulated LISA data sets.Comment: 10 pages, 4 figures, Updated for LISA 8 Symposium Proceeding

A Counterexample to Claimed COBE Constraints on Compact Toroidal Universe Models

It has been suggested that if the Universe satisfies a flat, multiply connected, perturbed Friedmann-Lema^itre model, then cosmic microwave background data from the COBE satellite implies that the minimum size of the injectivity diameter (shortest closed spatial geodesic) must be larger than about two fifths of the horizon diameter. To show that this claim is misleading, a simple $T^2 \times R$ universe model of injectivity diameter a quarter of this size, i.e. a tenth of the horizon diameter, is shown to be consistent with COBE four year observational maps of the cosmic microwave background. This is done using the identified circles principle.Comment: 11 pages, 3 figures, accepted for Classical & Quantum Gravit

On the formation of black holes in non-symmetric gravity

It has been recently suggested that the Non-symmetric Gravitational Theory (NGT) is free of black holes. Here, we study the linear version of NGT. We find that even with spherical symmetry the skew part of the metric is generally non-static. In addition, if the skew field is initially regular, it will remain regular everywhere and, in particular, at the horizon. Therefore, in the fully-nonlinear theory, if the initial skew-field is sufficiently small, the formation of a black hole is to be anticipated.Comment: 9 pages, ordinary LaTex

Pair of accelerated black holes in an anti-de Sitter background: the AdS C-metric

The anti-de Sitter C-metric (AdS C-metric) is characterized by a quite interesting new feature when compared with the C-metric in flat or de Sitter backgrounds. Indeed, contrarily to what happens in these two last exact solutions, the AdS C-metric only describes a pair of accelerated black holes if the acceleration parameter satisfies A>1/L, where L is the cosmological length. The two black holes cannot interact gravitationally and their acceleration is totally provided by the pressure exerted by a strut that pushes the black holes apart. Our analysis is based on the study of the causal structure, on the description of the solution in the AdS 4-hyperboloid in a 5D Minkowski embedding spacetime, and on the physics of the strut. We also analyze the cases A=1/L and A<1/L that represent a single accelerated black hole in the AdS background.Comment: 20 pages, 15 figures (RevTeX4). Published version: typo in fig. 5 corrected, references adde

Homoclinic chaos in the dynamics of a general Bianchi IX model

The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of saddle-center-center type in the finite region of phase space. This critical point engenders in the phase space dynamics the topology of stable and unstable four dimensional tubes $R \times S^3$, where $R$ is a saddle direction and $S^3$ is the manifold of unstable periodic orbits in the center-center sector. A general characteristic of the dynamical flow is an oscillatory mode about orbits of an invariant plane of the dynamics which contains the critical point and a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair of tubes (one stable, one unstable) emerging from the neighborhood of the critical point towards the FRW singularity have homoclinic transversal crossings. The homoclinic intersection manifold has topology $R \times S^2$ and is constituted of homoclinic orbits which are bi-asymptotic to the $S^3$ center-center manifold. This is an invariant signature of chaos in the model, and produces chaotic sets in phase space. The model also presents an asymptotic DeSitter attractor at infinity and initial conditions sets are shown to have fractal basin boundaries connected to the escape into the DeSitter configuration (escape into inflation), characterizing the critical point as a chaotic scatterer.Comment: 11 pages, 6 ps figures. Accepted for publication in Phys. Rev.

The gravitational wave rocket

Einstein's equations admit solutions corresponding to photon rockets. In these a massive particle recoils because of the anisotropic emission of photons. In this paper we ask whether rocket motion can be powered only by the emission of gravitational waves. We use the double series approximation method and show that this is possible. A loss of mass and gain in momentum arise in the second approximation because of the emission of quadrupole and octupole waves.Comment: 10 pages LaTe