JMP: General Relativity and Gravitation

Asymptotic stability of vacuum twisting type II metrics

Wlodzimierz Natorf
We generalize the result of Lukacs et al. on asymptotic stability of the Schwarzschild metric with respect to perturbations in the Robinson-Trautman class of metrics to the case of Petrov type II twisting metrics, under the condition of asymptotic flatness at future null infinity. The Bondi energy i ... [J. Math. Phys. 53, 022503 (2012)] published Tue Feb 7, 2012.

Spacelike hypersurfaces with negative total energy in de Sitter spacetime

Zhuobin Liang and Xiao Zhang
De Sitter spacetime can be separated into two parts along two kinds of hypersurfaces and the half-de Sitter spacetimes are covered by the planar and hyperbolic coordinates, respectively. Two positive energy theorems were proved previously for certain [script P]-asymptotically de Sitter and [script H ... [J. Math. Phys. 53, 022502 (2012)] published Fri Feb 3, 2012.

Quantum deformation of two four-dimensional spin foam models

Winston J. Fairbairn and Catherine Meusburger
We construct the q-deformed version of two four-dimensional spin foam models, the Euclidean and Lorentzian versions of the Engle, Pereira, Rovelli and Livine (EPRL) model. The q-deformed models are based on the representation theory of two copies of U([fraktur su](2)) at a root of unity and on the q ... [J. Math. Phys. 53, 022501 (2012)] published Thu Feb 2, 2012.

Inversion of a general hyperelliptic integral and particle motion in HoravaLifshitz black hole space-times

Victor Enolski, Betti Hartmann, Valeria Kagramanova, Jutta Kunz, Claus Lammerzahl et al.
The description of many dynamical problems such as the particle motion in higher dimensional spherically and axially symmetric space-times is reduced to the inversion of hyperelliptic integrals of all three kinds. The result of the inversion is defined locally, using the algebro-geometric techniques ... [J. Math. Phys. 53, 012504 (2012)] published Tue Jan 31, 2012.

Spinor representation for loop quantum gravity

Etera Livine and Johannes Tambornino
We perform a quantization of the loop gravity phase space purely in terms of spinorial variables, which have recently been shown to provide a direct link between spin network states and simplicial geometries. The natural Hilbert space to represent these spinors is the Bargmann space of holomorphic s ... [J. Math. Phys. 53, 012503 (2012)] published Fri Jan 20, 2012.

Relative entropy as a measure of inhomogeneity in general relativity

Nikolas Akerblom and Gunther Cornelissen
We introduce the notion of relative volume entropy for two spacetimes with preferred compact spacelike foliations. This is accomplished by applying the notion of Kullback-Leibler divergence to the volume elements induced on spacelike slices. The resulting quantity gives a lower bound on the number o ... [J. Math. Phys. 53, 012502 (2012)] published Tue Jan 10, 2012.

Static solutions from the point of view of comparison geometry

Martin Reiris
We analyze (the harmonic map representation of) static solutions of the Einstein equations in dimension three from the point of view of comparison geometry. We find simple monotonic quantities capturing sharply the influence of the Lapse function on the focussing of geodesics. This allows, in partic ... [J. Math. Phys. 53, 012501 (2012)] published Thu Jan 5, 2012.

Lorentzian covering space and homotopy classes

Do-Hyung Kim
We analyze structures of covering space over a Lorentzian manifold. By use of this we show that, if a Lorentzian manifold is globally hyperbolic then for any two causally related points p and q, the number of homotopy classes of causal curves from p to q is finite and each of its homotopy classes ha ... [J. Math. Phys. 52, 122501 (2011)] published Tue Dec 20, 2011.

Global hyperbolicity is stable in the interval topology

J. J. Benavides Navarro and E. Minguzzi
We prove that global hyperbolicity is stable in the interval topology on the spacetime metrics. We also prove that every globally hyperbolic spacetime admits a Cauchy hypersurface which remains Cauchy under small perturbations of the spacetime metric. Moreover, we prove that if the spacetime admits ... [J. Math. Phys. 52, 112504 (2011)] published Fri Nov 18, 2011.

Sphere orderings representation of space-time

M. Vatandoost and Y. Bahrampour
A space-time may be regarded as a partially ordered set by causal relations. R. J. Low considered a continuous sphere order representation of a space-time and obtained some interesting results. However, some important questions about the conditions of continuity of this representation are still left ... [J. Math. Phys. 52, 112503 (2011)] published Thu Nov 17, 2011.

Dirac spinors in Bianchi-I f(R)-cosmology with torsion

Stefano Vignolo, Luca Fabbri, and Roberto Cianci
We study Dirac spinors in Bianchi type-I cosmological models, within the framework of torsional f(R)-gravity. We find four types of results: the resulting dynamic behavior of the universe depends on the particular choice of function f(R); some f(R) models do not isotropize and have no Einstein limit ... [J. Math. Phys. 52, 112502 (2011)] published Fri Nov 11, 2011.

Maximal slicings in spherical symmetry: Local existence and construction

Isabel Cordero-Carrion, Jose Maria Ibanez, and Juan Antonio Morales-Lladosa
We show that any spherically symmetric spacetime locally admits a maximal space-like slicing and we give a procedure allowing its construction. The designed construction procedure is based on purely geometrical arguments and, in practice, leads to solve a decoupled system of first-order quasi-linear ... [J. Math. Phys. 52, 112501 (2011)] published Thu Nov 10, 2011.

Velocity and heat flow in a composite two fluid system

J. P. Krisch and E. N. Glass
We describe the stress energy of a fluid with two unequal stresses and heat flow in terms of two perfect fluid components. The description is in terms of the fluid velocity overlap of the components, and makes no assumptions about the equations of state of the perfect fluids. The description is appl ... [J. Math. Phys. 52, 102503 (2011)] published Tue Oct 25, 2011.

On the stability of the massive scalar field in Kerr space-time

Horst Reinhard Beyer
The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon equation, describing the propagation of a scalar field in the ba ... [J. Math. Phys. 52, 102502 (2011)] published Fri Oct 21, 2011.

Lensing by Kerr black holes. II: Analytical study of quasi-equatorial lensing observables

Amir B. Aazami, Charles R. Keeton, and A. O. Petters
In this second paper, we develop an analytical theory of quasi-equatorial lensing by Kerr black holes. In this setting we solve perturbatively our general lens equation with displacement given in Paper I, going beyond weak-deflection Kerr lensing to third order in our expansion parameter epsilon, wh ... [J. Math. Phys. 52, 102501 (2011)] published Tue Oct 11, 2011.

Lensing by Kerr black holes. I. General lens equation and magnification formula

Amir B. Aazami, Charles R. Keeton, and A. O. Petters
We develop a unified, analytic framework for gravitational lensing by Kerr black holes. In this first paper, we present a new, general lens equation and magnification formula governing lensing by a compact object. Our lens equation assumes that the source and observer are in the asymptotically flat ... [J. Math. Phys. 52, 092502 (2011)] published Wed Sep 28, 2011.

On holographic realization of logarithmic Galilean conformal algebra

Ali Hosseiny and Ali Naseh
We study two-dimensional logarithmic Galilean conformal algebra (LGCA) by making use of a contraction of topologically massive gravity at critical point. We observe that using a naive contraction at the critical point fails to give a well defined theory, though contracting the theory while we are ap ... [J. Math. Phys. 52, 092501 (2011)] published Wed Sep 21, 2011.

Classical gauge theory in Riem

Henrique de A. Gomes
In the geometrodynamical setting of general relativity in Lagrangian form, the objects of study are the Riemannian metrics (and their time derivatives) over a given 3-manifold M. It is our aim in this paper to study some geometrical aspects of the space [script M]:=Riem(M) of all metrics over M. For ... [J. Math. Phys. 52, 082501 (2011)] published Fri Aug 12, 2011.

4-dimensional spin-foam model with quantum Lorentz group

Muxin Han
We study the quantum group deformation of the Lorentzian EPRL spin-foam model. The construction uses the harmonic analysis on the quantum Lorentz group. We show that the quantum group spin-foam model so defined is free of the infra-red divergence, thus gives a finite partition function on a fixed tr ... [J. Math. Phys. 52, 072501 (2011)] published Mon Jul 11, 2011.

Gravity from the extension of spatial diffeomorphisms

Szilard Farkas and Emil J. Martinec
The possibility of the extension of spatial diffeomorphisms to a larger family of symmetries in a class of classical field theories is studied. The generator of the additional local symmetry contains a quadratic kinetic term and a potential term which can be a general (not necessarily local) functio ... [J. Math. Phys. 52, 062501 (2011)] published Fri Jun 24, 2011.

Refocusing of light rays in space-time

Paul A. Kinlaw
We discuss several definitions of refocusing of null-geodesics in a strongly causal space-time and prove their equivalence. A space-time which is strongly refocusing at a point x is refocusing at x. Examples are provided of space-times which are refocusing at a point x but not strongly refocusing at ... [J. Math. Phys. 52, 052505 (2011)] published Tue May 31, 2011.