123 research outputs found
Comment on Ricci Collineations for type B warped space-times
We present two counterexamples to the paper by Carot et al. in Gen. Rel.
Grav. 1997, 29, 1223 and show that the results obtained are correct but not
general.Comment: LaTex, 3 pages, Eq. (9) and reference added, typos corrected; Gen.
Rel. Grav (to appear
On the general structure of Ricci collineations for type B warped spacetimes
A complete study of the structure of Ricci collineations for type B warped
spacetimes is carried out. This study can be used as a method to obtain these
symetries in such spacetimes. Special cases as 2+2 reducible spacetimes, and
plane and spherical symmetric spacetimes are considered specifically.Comment: 18 pages. Version accepted for publication in JM
Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models
The consistency of the constraint with the evolution equations for spatially
inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands
that the former are preserved along the timelike congruence represented by the
velocity of the dust fluid, leading to \emph{new} non-trivial constraints. This
fact has been used to conjecture that the resulting models correspond to the
spatially homogeneous (SH) models of Bianchi type I, at least for the case
where the cosmological constant vanish. By exploiting the full set of the
constraint equations as expressed in the 1+3 covariant formalism and using
elements from the theory of the spacelike congruences, we provide a direct and
simple proof of this conjecture for vacuum and dust fluid models, which shows
that the Szekeres family of solutions represents the most general class of SIIS
models. The suggested procedure also shows that, the uniqueness of the SIIS of
the Petrov type D is not, in general, affected by the presence of a non-zero
pressure fluid. Therefore, in order to allow a broader class of Petrov type I
solutions apart from the SH models of Bianchi type I, one should consider more
general ``silent'' configurations by relaxing the vanishing of the vorticity
and the magnetic part of the Weyl tensor but maintaining their ``silence''
properties i.e. the vanishing of the curls of and the pressure
.Comment: Latex, 19 pages, no figures;(v2) some clarification remarks and an
appendix are added; (v3) minor changes to match published versio
Note on Matter Collineations in Kantowski-Sachs, Bianchi Types I and III Spacetimes
We show that the classification of Kantowski-Sachs, Bianchi Types I and III
spacetimes admitting Matter Collineations (MCs) presented in a recent paper by
Camci et al. [Camci, U., and Sharif, M. {Matter Collineations in
Kantowski-Sachs, Bianchi Types I and III Spacetimes}, 2003 Gen. Relativ. Grav.
vol. 35, 97-109] is incomplete. Furthermore for these spacetimes and when the
Einstein tensor is non-degenerate, we give the complete Lie Algebra of MCs and
the algebraic constraints on the spatial components of the Einstein tensor.Comment: 10 pages, Latex. Accepted for publication in General Relativity and
Gravitatio
A classification of spherically symmetric spacetimes
A complete classification of locally spherically symmetric four-dimensional
Lorentzian spacetimes is given in terms of their local conformal symmetries.
The general solution is given in terms of canonical metric types and the
associated conformal Lie algebras. The analysis is based upon the local
conformal decomposition into 2+2 reducible spacetimes and the Petrov type. A
variety of physically meaningful example spacetimes are discussed
Ricci Collineations for type B warped space-times
We present the general structure of proper Ricci Collineations (RC) for type
B warped space-times. Within this framework, we give a detailed description of
the most general proper RC for spherically symmetric metrics. As examples,
static spherically symmetric and Friedmann-Robertson-Walker space-times are
considered.Comment: 18 pages, Latex, To appear in GR
Flat deformation theorem and symmetries in spacetime
The \emph{flat deformation theorem} states that given a semi-Riemannian
analytic metric on a manifold, locally there always exists a two-form ,
a scalar function , and an arbitrarily prescribed scalar constraint
depending on the point of the manifold and on and , say , such that the \emph{deformed metric} is
semi-Riemannian and flat. In this paper we first show that the above result
implies that every (Lorentzian analytic) metric may be written in the
\emph{extended Kerr-Schild form}, namely where is flat and are two null covectors such that
; next we show how the symmetries of are connected to those of
, more precisely; we show that if the original metric admits a
Conformal Killing vector (including Killing vectors and homotheties), then the
deformation may be carried out in a way such that the flat deformed metric
`inherits' that symmetry.Comment: 30 pages, 0 figure
Spacelike Ricci Inheritance Vectors in a Model of String Cloud and String Fluid Stress Tensor
We study the consequences of the existence of spacelike Ricci inheritance
vectors (SpRIVs) parallel to for model of string cloud and string fluid
stress tensor in the context of general relativity. Necessary and sufficient
conditions are derived for a spacetime with a model of string cloud and string
fluid stress tensor to admit a SpRIV and a SpRIV which is also a spacelike
conformal Killing vector (SpCKV). Also, some results are obtained.Comment: 11 page
Kinematic self-similar locally rotationally symmetric models
A brief summary of results on kinematic self-similarities in general
relativity is given. Attention is focussed on locally rotationally symmetric
models admitting kinematic self-similar vectors. Coordinate expressions for the
metric and the kinematic self-similar vector are provided.
Einstein's field equations for perfect fluid models are investigated and all
the homothetic perfect fluid solutions admitting a maximal four-parameter group
of isometries are given.Comment: 12 pages, LaTeX, final version, to appear in Class. Quantum Gra
Classification of Spherically Symmetric Static Spacetimes according to their Matter Collineations
The spherically symmetric static spacetimes are classified according to their
matter collineations. These are studied when the energy-momentum tensor is
degenerate and also when it is non-degenerate. We have found a case where the
energy-momentum tensor is degenerate but the group of matter collineations is
finite. For the non-degenerate case, we obtain either {\it four}, {\it five},
{\it six} or {\it ten} independent matter collineations in which four are
isometries and the rest are proper. We conclude that the matter collineations
coincide with the Ricci collineations but the constraint equations are
different which on solving can provide physically interesting cosmological
solutions.Comment: 15 pages, no figure, Late
- …