Isotropy, shear, symmetry and exact solutions for relativistic fluid spheres

The symmetry method is used to derive solutions of Einstein's equations for fluid spheres using an isotropic metric and a velocity four vector that is non-comoving. Initially the Lie, classical approach is used to review and provide a connecting framework for many comoving and so shear free solutions. This provides the basis for the derivation of the classical point symmetries for the more general and mathematicaly less tractable description of Einstein's equations in the non-comoving frame. Although the range of symmetries is restrictive, existing and new symmetry solutions with non-zero shear are derived. The range is then extended using the non-classical direct symmetry approach of Clarkson and Kruskal and so additional new solutions with non-zero shear are also presented. The kinematics and pressure, energy density, mass function of these solutions are determined.Comment: To appear in Classical and Quantum Gravit

Purely electromagnetic spacetimes

Electrovacuum solutions devoid of usual mass sources are classified in the case of one, two and three commuting Killing vectors. Three branches of solutions exist. Electromagnetically induced mass terms appear in some of them.Comment: 8 page

Natural extension of the Generalised Uncertainty Principle

We discuss a gedanken experiment for the simultaneous measurement of the position and momentum of a particle in de Sitter spacetime. We propose an extension of the so-called generalized uncertainty principle (GUP) which implies the existence of a minimum observable momentum. The new GUP is directly connected to the nonzero cosmological constant, which becomes a necessary ingredient for a more complete picture of the quantum spacetime.Comment: 4 pages, 1 figure, v2 with added references, revised and extended as published in CQ

An Iterative Approach to Twisting and Diverging, Type N, Vacuum Einstein Equations: A (Third-Order) Resolution of Stephani's `Paradox'

In 1993, a proof was published, within ``Classical and Quantum Gravity,'' that there are no regular solutions to the {\it linearized} version of the twisting, type-N, vacuum solutions of the Einstein field equations. While this proof is certainly correct, we show that the conclusions drawn from that fact were unwarranted, namely that this irregularity caused such solutions not to be able to truly describe pure gravitational waves. In this article, we resolve the paradox---since such first-order solutions must always have singular lines in space for all sufficiently large values of $r$---by showing that if we perturbatively iterate the solution up to the third order in small quantities, there are acceptable regular solutions. That these solutions become flat before they become non-twisting tells us something interesting concerning the general behavior of solutions describing gravitational radiation from a bounded source.Comment: 11 pages, a plain TeX file, submitted to ``Classical and Quantum Gravity'

Instability of the negative mass Schwarzschild naked singularity

We study the negative mass Schwarzschild spacetime, which has a naked singularity, and show that it is perturbatively unstable. This is achieved by first introducing a modification of the well known Regge - Wheeler - Zerilli approach to black hole perturbations to allow for the presence of a ``kinematic'' singularity that arises for negative masses, and then exhibiting exact exponentially growing solutions to the linearized Einstein's equations. The perturbations are smooth everywhere and behave nicely around the singularity and at infinity. In particular, the first order variation of the scalar invariants can be made everywhere arbitrarily small as compared to the zeroth order terms. Our approach is also compared to a recent analysis that leads to a different conclusion regarding the stability of the negative mass Schwarzschild spacetime. We also comment on the relevance of our results to the stability of more general negative mass, nakedly singular spacetimes.Comment: 15 page

Time-Periodic Solutions of the Einstein's Field Equations II

In this paper, we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish, keep finite or take the infinity at some points in these space-times, respectively. The singularities of these new time-periodic solutions are investigated and some new physical phenomena are found. The applications of these solutions in modern cosmology and general relativity can be expected.Comment: 10 pages, 1 figur

New first integral for twisting type-N vacuum gravitational fields with two non-commuting Killing vectors

A new first integral for the equations corresponding to twisting type-N vacuum gravitational fields with two non-commuting Killing vectors is introduced. A new reduction of the problem to a complex second-order ordinary differential equation is given. Alternatively, the mentioned first integral can be used in order to provide a first integral of the second-order complex equation introduced in a previous treatment of the problem.Comment: 7 pages, LaTeX, uses ioplppt.sty and iopl12.sty; to be published in Class. Quantum Gra

Brans-Dicke cylindrical wormholes

Static axisymmetric thin-shell wormholes are constructed within the framework of the Brans-Dicke scalar-tensor theory of gravity. Examples of wormholes associated with vacuum and electromagnetic fields are studied. All constructions must be threaded by exotic matter, except in the case of geometries with a singularity of finite radius, associated with an electric field, which can have a throat supported by ordinary matter. These results are achieved with any of the two definitions of the flare-out condition considered.Comment: 11 pages, 3 figures; v3: corrected version, conclusions unchange

Realistic fluids as source for dynamically accreting black holes in a cosmological background

We show that a single imperfect fluid can be used as a source to obtain the generalized McVittie metric as an exact solution to Einstein's equations. The mass parameter in this metric varies with time thanks to a mechanism based on the presence of a temperature gradient. This fully dynamical solution is interpreted as an accreting black hole in an expanding universe if the metric asymptotes to Schwarzschild-de Sitter at temporal infinity. We present a simple but instructive example for the mass function and briefly discuss the structure of the apparent horizons and the past singularity.Comment: 5 pages, 2 figures. Updated references and minor changes to match the version accepted for publishing in PR