66,108 research outputs found
Self-similar static solutions admitting a two-space of constant curvature
A recent result by Haggag and Hajj-Boutros is reviewed within the framework
of self-similar space-times, extending, in some sense, their results and
presenting a family of metrics consisting of all the static spherically
symmetric perfect fluid solutions admitting a homothety.Comment: 6 page
On the Theory of Killing Orbits in Space-Time
This paper gives a theoretical discussion of the orbits and isotropies which
arise in a space-time which admits a Lie algebra of Killing vector fields. The
submanifold structure of the orbits is explored together with their induced
Killing vector structure. A general decomposition of a space-time in terms of
the nature and dimension of its orbits is given and the concept of stability
and instability for orbits introduced. A general relation is shown linking the
dimensions of the Killing algebra, the orbits and the isotropies. The
well-behaved nature of "stable" orbits and the possible miss-behaviour of the
"unstable" ones is pointed out and, in particular, the fact that independent
Killing vector fields in space-time may not induce independent such vector
fields on unstable orbits. Several examples are presented to exhibit these
features. Finally, an appendix is given which revisits and attempts to clarify
the well-known theorem of Fubini on the dimension of Killing orbits.Comment: Latex, 19 pages, no figur
The principle of equivalence and projective structure in space-times
This paper discusses the extent to which one can determine the space-time
metric from a knowledge of a certain subset of the (unparametrised) geodesics
of its Levi-Civita connection, that is, from the experimental evidence of the
equivalence principle. It is shown that, if the space-time concerned is known
to be vacuum, then the Levi-Civita connection is uniquely determined and its
associated metric is uniquely determined up to a choice of units of
measurement, by the specification of these geodesics. It is further
demonstrated that if two space-times share the same unparametrised geodesics
and only one is assumed vacuum then their Levi-Civita connections are again
equal (and so the other metric is also a vacuum metric) and the first result
above is recovered.Comment: 23 pages, submitted to Classical and Quantum Gravit
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
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
Limits of space-times in five dimensions and their relation to the Segre Types
A limiting diagram for the Segre classification in 5-dimensional space-times
is obtained, extending a recent work on limits of the energy-momentum tensor in
general relativity. Some of Geroch's results on limits of space-times in
general relativity are also extended to the context of five-dimensional
Kaluza-Klein space-times.Comment: Late
Limits of the energy-momentum tensor in general relativity
A limiting diagram for the Segre classification of the energy-momentum tensor
is obtained and discussed in connection with a Penrose specialization diagram
for the Segre types. A generalization of the coordinate-free approach to limits
of Paiva et al. to include non-vacuum space-times is made. Geroch's work on
limits of space-times is also extended. The same argument also justifies part
of the procedure for classification of a given spacetime using Cartan scalars.Comment: LaTeX, 21 page
Manufacturing time operators: covariance, selection criteria, and examples
We provide the most general forms of covariant and normalized time operators
and their probability densities, with applications to quantum clocks, the time
of arrival, and Lyapunov quantum operators. Examples are discussed of the
profusion of possible operators and their physical meaning. Criteria to define
unique, optimal operators for specific cases are given
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
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