Scalar Polynomial Singularities in Power-Law Spacetimes

Recently, Helliwell and Konkowski (\texttt{gr-qc/0701149}) have examined the quantum "healing" of some classical singularities in certain power-law spacetimes. Here I further examine classical properties of these spacetimes and show that some of them contain naked strong curvature singularities.Comment: 7 pages revtex4 two figures extended discussio

A note on cosmological Levi-Civita spacetimes in higher dimensions

We find a class of solutions to cosmological Einstein equations that generalizes the four dimensional cylindrically symmetric spacetimes to higher dimensions. The AdS soliton is a special member of this class with a unique singularity structure.Comment: 3 pages; version to appear in Phys. Rev.

Cylindrical solutions in braneworld gravity

In this article we investigate exact cylindrically symmetric solutions to the modified Einstein field equations in the brane world gravity scenarios. It is shown that for the special choice of the equation of state $2U+P=0$ for the dark energy and dark pressure, the solutions found could be considered formally as solutions of the Einstein-Maxwell equations in 4-D general relativity.Comment: 12 pages, RevTex format, typos corrected and references added. Accepted for publication in PR

Tetrads in Geometrodynamics

A new tetrad is introduced within the framework of geometrodynamics for non-null electromagnetic fields. This tetrad diagonalizes the electromagnetic stress-energy tensor and allows for maximum simplification of the expression of the electromagnetic field. The Einstein-Maxwell equations will also be simplified

Generating Static Fluid Spheres by Conformal Transformations

We generate an explicit four-fold infinity of physically acceptable exact perfect fluid solutions of Einstein's equations by way of conformal transformations of physically unacceptable solutions (one way to view the use of isotropic coordinates). Special cases include the Schwarzschild interior solution and the Einstein static universe. The process we consider involves solving two equations of the Riccati type coupled by a single generating function rather than a specification of one of the two metric functions.Comment: 4 pages revtex4, two figures, Final form to appear in Phys. Rev.

Generating perfect fluid spheres in general relativity

Ever since Karl Schwarzschild's 1916 discovery of the spacetime geometry describing the interior of a particular idealized general relativistic star -- a static spherically symmetric blob of fluid with position-independent density -- the general relativity community has continued to devote considerable time and energy to understanding the general-relativistic static perfect fluid sphere. Over the last 90 years a tangle of specific perfect fluid spheres has been discovered, with most of these specific examples seemingly independent from each other. To bring some order to this collection, in this article we develop several new transformation theorems that map perfect fluid spheres into perfect fluid spheres. These transformation theorems sometimes lead to unexpected connections between previously known perfect fluid spheres, sometimes lead to new previously unknown perfect fluid spheres, and in general can be used to develop a systematic way of classifying the set of all perfect fluid spheres.Comment: 18 pages, 4 tables, 4 figure

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

Timelike and Spacelike Matter Inheritance Vectors in Specific Forms of Energy-Momentum Tensor

This paper is devoted to the investigation of the consequences of timelike and spacelike matter inheritance vectors in specific forms of energy-momentum tensor, i.e., for string cosmology (string cloud and string fluid) and perfect fluid. Necessary and sufficient conditions are developed for a spacetime with string cosmology and perfect fluid to admit a timelike matter inheritance vector, parallel to $u^a$ and spacelike matter inheritance vector, parallel to $x^a$. We compare the outcome with the conditions of conformal Killing vectors. This comparison provides us the conditions for the existence of matter inheritance vector when it is also a conformal Killing vector. Finally, we discuss these results for the existence of matter inheritance vector in the special cases of the above mentioned spacetimes.Comment: 27 pages, accepted for publication in Int. J. of Mod. Phys.

Photon rockets moving arbitrarily in any dimension

A family of explicit exact solutions of Einstein's equations in four and higher dimensions is studied which describes photon rockets accelerating due to an anisotropic emission of photons. It is possible to prescribe an arbitrary motion, so that the acceleration of the rocket need not be uniform - both its magnitude and direction may vary with time. Except at location of the point-like rocket the spacetimes have no curvature singularities, and topological defects like cosmic strings are also absent. Any value of a cosmological constant is allowed. We investigate some particular examples of motion, namely a straight flight and a circular trajectory, and we derive the corresponding radiation patterns and the mass loss of the rockets. We also demonstrate the absence of "gravitational aberration" in such spacetimes. This interesting member of the higher-dimensional Robinson-Trautman class of pure radiation spacetimes of algebraic type D generalises the class of Kinnersley's solutions that has long been known in four-dimensional general relativity.Comment: Text and figures modified (22 pages, 8 figures). To appear in the International Journal of Modern Physics D, Vol. 20, No..

A new time-machine model with compact vacuum core

We present a class of curved-spacetime vacuum solutions which develope closed timelike curves at some particular moment. We then use these vacuum solutions to construct a time-machine model. The causality violation occurs inside an empty torus, which constitutes the time-machine core. The matter field surrounding this empty torus satisfies the weak, dominant, and strong energy conditions. The model is regular, asymptotically-flat, and topologically-trivial. Stability remains the main open question.Comment: 7 page