349 research outputs found
On the completeness of impulsive gravitational wave space-times
We consider a class of impulsive gravitational wave space-times, which
generalize impulsive pp-waves. They are of the form ,
where is a Riemannian manifold of arbitrary dimension and carries
the line element with the line
element of and the Dirac measure. We prove a completeness result
for such space-times with complete Riemannian part .Comment: 13 pages, minor changes suggested by the referee
Singularity-Free Cylindrical Cosmological Model
A cylindrically symmetric perfect fluid spacetime with no curvature
singularity is shown. The equation of state for the perfect fluid is that of a
stiff fluid. The metric is diagonal and non-separable in comoving coordinates
for the fluid. It is proven that the spacetime is geodesically complete and
globally hyperbolic.Comment: LaTeX 2e, 8 page
Non-singular radiation cosmological models
In this paper we analyse the possibility of constructing singularity-free
inhomogeneous cosmological models with a pure radiation field as matter
content. It is shown that the conditions for regularity are very easy to
implement and therefore there is a huge number of such spacetimes.Comment: 13 pages, LaTex, ws-mpla, to appear in Modern Physics Letters
Exterior Differential System for Cosmological G2 Perfect Fluids and Geodesic Completeness
In this paper a new formalism based on exterior differential systems is
derived for perfect-fluid spacetimes endowed with an abelian orthogonally
transitive G2 group of motions acting on spacelike surfaces. This formulation
allows simplifications of Einstein equations and it can be applied for
different purposes. As an example a singularity-free metric is rederived in
this framework. A sufficient condition for a diagonal metric to be geodesically
complete is also provided.Comment: 27 pages, 0 figures, LaTeX2e, to be published in Classical and
Quantum Gravit
The Lorentzian distance formula in noncommutative geometry
For almost twenty years, a search for a Lorentzian version of the well-known
Connes' distance formula has been undertaken. Several authors have contributed
to this search, providing important milestones, and the time has now come to
put those elements together in order to get a valid and functional formula.
This paper presents a historical review of the construction and the proof of a
Lorentzian distance formula suitable for noncommutative geometry.Comment: 16 pages, final form, few references adde
Aspects of noncommutative Lorentzian geometry for globally hyperbolic spacetimes
Connes' functional formula of the Riemannian distance is generalized to the
Lorentzian case using the so-called Lorentzian distance, the d'Alembert
operator and the causal functions of a globally hyperbolic spacetime. As a step
of the presented machinery, a proof of the almost-everywhere smoothness of the
Lorentzian distance considered as a function of one of the two arguments is
given. Afterwards, using a -algebra approach, the spacetime causal
structure and the Lorentzian distance are generalized into noncommutative
structures giving rise to a Lorentzian version of part of Connes'
noncommutative geometry. The generalized noncommutative spacetime consists of a
direct set of Hilbert spaces and a related class of -algebras of
operators. In each algebra a convex cone made of self-adjoint elements is
selected which generalizes the class of causal functions. The generalized
events, called {\em loci}, are realized as the elements of the inductive limit
of the spaces of the algebraic states on the -algebras. A partial-ordering
relation between pairs of loci generalizes the causal order relation in
spacetime. A generalized Lorentz distance of loci is defined by means of a
class of densely-defined operators which play the r\^ole of a Lorentzian
metric. Specializing back the formalism to the usual globally hyperbolic
spacetime, it is found that compactly-supported probability measures give rise
to a non-pointwise extension of the concept of events.Comment: 43 pages, structure of the paper changed and presentation strongly
improved, references added, minor typos corrected, title changed, accepted
for publication in Reviews in Mathematical Physic
On global models for isolated rotating axisymmetric charged bodies; uniqueness of the exterior field
A relatively recent study by Mars and Senovilla provided us with a uniqueness
result for the exterior vacuum gravitational field generated by an isolated
distribution of matter in axial rotation in equilibrium in General Relativity.
The generalisation to exterior electrovacuum gravitational fields, to include
charged rotating objects, is presented here.Comment: LaTeX, 21 pages, uses iopart styl
Fermat Principle in Finsler Spacetimes
It is shown that, on a manifold with a Finsler metric of Lorentzian
signature, the lightlike geodesics satisfy the following variational principle.
Among all lightlike curves from a point (emission event) to a timelike curve
(worldline of receiver), the lightlike geodesics make the arrival time
stationary. Here ``arrival time'' refers to a parametrization of the timelike
curve. This variational principle can be applied (i) to the vacuum light rays
in an alternative spacetime theory, based on Finsler geometry, and (ii) to
light rays in an anisotropic non-dispersive medium with a general-relativistic
spacetime as background.Comment: 18 pages, submitted to Gen. Rel. Gra
Klein-Gordon Solutions on Non-Globally Hyperbolic Standard Static Spacetimes
We construct a class of solutions to the Cauchy problem of the Klein-Gordon
equation on any standard static spacetime. Specifically, we have constructed
solutions to the Cauchy problem based on any self-adjoint extension (satisfying
a technical condition: "acceptability") of (some variant of) the
Laplace-Beltrami operator defined on test functions in an -space of the
static hypersurface. The proof of the existence of this construction completes
and extends work originally done by Wald. Further results include the
uniqueness of these solutions, their support properties, the construction of
the space of solutions and the energy and symplectic form on this space, an
analysis of certain symmetries on the space of solutions and of various
examples of this method, including the construction of a non-bounded below
acceptable self-adjoint extension generating the dynamics
The causal ladder and the strength of K-causality. I
A unifying framework for the study of causal relations is presented. The
causal relations are regarded as subsets of M x M and the role of the
corresponding antisymmetry conditions in the construction of the causal ladder
is stressed. The causal hierarchy of spacetime is built from chronology up to
K-causality and new characterizations of the distinction and strong causality
properties are obtained. The closure of the causal future is not transitive, as
a consequence its repeated composition leads to an infinite causal subladder
between strong causality and K-causality - the A-causality subladder. A
spacetime example is given which proves that K-causality differs from infinite
A-causality.Comment: 16 pages, one figure. Old title: ``On the relationship between
K-causality and infinite A-causality''. Some typos fixed; small change in the
proof of lemma 4.
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