A Smooth Lattice construction of the Oppenheimer-Snyder spacetime

We present test results for the smooth lattice method using an Oppenheimer-Snyder spacetime. The results are in excellent agreement with theory and numerical results from other authors.Comment: 60 pages, 28 figure

Shells around black holes: the effect of freely specifiable quantities in Einstein's constraint equations

We solve Einstein's constraint equations in the conformal thin-sandwich decomposition to model thin shells of non-interacting particles in circular orbit about a non-rotating black hole. We use these simple models to explore the effects of some of the freely specifiable quantities in this decomposition on the physical content of the solutions. Specifically, we adopt either maximal slicing or Kerr-Schild slicing, and make different choices for the value of the lapse on the black hole horizon. For one particular choice of these quantities the resulting equations can be solved analytically; for all others we construct numerical solutions. We find that these different choices have no effect on our solutions when they are expressed in terms of gauge-invariant quantities.Comment: 9 pages, 4 figure

Vacuum Polarization of a Massless Scalar Field in the Background of a Global Monopole with Finite Core

In this paper we analyze the vacuum polarization effects of a massless scalar field in the background of a global monopole considering a inner structure to it. Specifically we investigate the effect of its structure on the vacuum expectation value of the square of the field operator, , admitting a non-minimal coupling between the field with the geometry: $\xi {\cal{R}}\hat{\Phi}^2$. Also we calculate the corrections on the vacuum expectation value of the energy-momentum tensor, , due to the inner structure of the monopole. In order to develop these analysis, we calculate the Euclidean Green function associated with the system for points in the region outside the core. As we shall see, for specific value of the coupling parameter $\xi$, the corrections caused by the inner structure of the monopole can provide relevant contributions on these vacuum polarizations.Comment: Accepted for publication in Classical and Quantum Gravity. Added references. 22 pages, 1 figur

Effects of Electromagnetic Field on the Dynamical Instability of Cylindrical Collapse

The objective of this paper is to discuss the dynamical instability in the context of Newtonian and post Newtonian regimes. For this purpose, we consider non-viscous heat conducting charged isotropic fluid as a collapsing matter with cylindrical symmetry. Darmois junction conditions are formulated. The perturbation scheme is applied to investigate the influence of dissipation and electromagnetic field on the dynamical instability. We conclude that the adiabatic index $\Gamma$ has smaller value for such a fluid in cylindrically symmetric than isotropic sphere

Effective gravitational equations for f(R) braneworld models

The viability of achieving gravitational consistent braneworld models in the framework of a f(R) theory of gravity is investigated. After a careful generalization of the usual junction conditions encompassing the embedding of the 3-brane into a f(R) bulk, we provide a prescription giving the necessary constraints in order to implement the projected second order effective field equations on the brane.Comment: 15 pages, no figures. Accepted for publication in the Physical Review

Magnetic Surfaces in Stationary Axisymmetric General Relativity

In this paper a new method is derived for constructing electromagnetic surface sources for stationary axisymmetric electrovac spacetimes endowed with non-smooth or even discontinuous Ernst potentials. This can be viewed as a generalization of some classical potential theory results, since lack of continuity of the potential is related to dipole density and lack of smoothness, to monopole density. In particular this approach is useful for constructing the dipole source for the magnetic field. This formalism involves solving a linear elliptic differential equation with boundary conditions at infinity. As an example, two different models of surface densities for the Kerr-Newman electrovac spacetime are derived.Comment: 15 page

Self-gravitating branes of codimension 4 in Lovelock gravity

We construct a familly of exact solutions of Lovelock equations describing codimension four branes with discrete symmetry in the transverse space. Unlike what is known from pure Einstein gravity, where such brane solutions of higher codimension are singular, the solutions we find, for the complete Lovelock theory, only present removable singularities. The latter account for a localised tension-like energy-momentum tensor on the brane, in analogy with the case of a codimension two self-gravitating cosmic string in pure Einstein gravity. However, the solutions we discuss present two main distinctive features : the tension of the brane receives corrections from the induced curvature of the brane's worldsheet and, in a given Lovelock theory, the spectrum of possible values of the tension is discrete. These solutions provide a new framework for the study of higher codimension braneworlds.Comment: 22 page

Gravitational collapse in asymptotically Anti-de Sitter/de Sitter backgrounds

We study here the gravitational collapse of a matter cloud with a non-vanishing tangential pressure in the presence of a non-zero cosmological term. Conditions for bounce and singularity formation are derived for the model. It is also shown that when the tangential pressures vanish, the bounce and singularity conditions reduce to that of the dust case studied earlier. The collapsing interior is matched with an exterior which is asymptotically de Sitter or anti de Sitter, depending on the sign of cosmological constant. The junction conditions for matching the cloud to exterior are specified. The effect of the cosmological term on apparent horizons is studied in some detail, and the nature of central singularity is analyzed. We also discuss here the visibility of the singularity and implications for the cosmic censorship conjecture.Comment: 11 pages, 1 figure, Revtex

On the entropy production of time series with unidirectional linearity

There are non-Gaussian time series that admit a causal linear autoregressive moving average (ARMA) model when regressing the future on the past, but not when regressing the past on the future. The reason is that, in the latter case, the regression residuals are only uncorrelated but not statistically independent of the future. In previous work, we have experimentally verified that many empirical time series indeed show such a time inversion asymmetry. For various physical systems, it is known that time-inversion asymmetries are linked to the thermodynamic entropy production in non-equilibrium states. Here we show that such a link also exists for the above unidirectional linearity. We study the dynamical evolution of a physical toy system with linear coupling to an infinite environment and show that the linearity of the dynamics is inherited to the forward-time conditional probabilities, but not to the backward-time conditionals. The reason for this asymmetry between past and future is that the environment permanently provides particles that are in a product state before they interact with the system, but show statistical dependencies afterwards. From a coarse-grained perspective, the interaction thus generates entropy. We quantitatively relate the strength of the non-linearity of the backward conditionals to the minimal amount of entropy generation.Comment: 16 page

Rotating perfect fluid sources of the NUT metric

Locally rotationally symmetric perfect fluid solutions of Einstein's gravitational equations are matched along the hypersurface of vanishing pressure with the NUT metric. These rigidly rotating fluids are interpreted as sources for the vacuum exterior which consists only of a stationary region of the Taub-NUT space-time. The solution of the matching conditions leaves generally three parameters in the global solution. Examples of perfect fluid sources are discussed.Comment: 8 pages, late