745 research outputs found
On the causal properties of warped product spacetimes
It is shown that the warped product spacetime P=M *_f H, where H is a
complete Riemannian manifold, and the original spacetime M share necessarily
the same causality properties, the only exceptions being the properties of
causal continuity and causal simplicity which present some subtleties. For
instance, it is shown that if diamH=+\infty, the direct product spacetime P=M*H
is causally simple if and only if (M,g) is causally simple, the Lorentzian
distance on M is continuous and any two causally related events at finite
distance are connected by a maximizing geodesic. Similar conditions are found
for the causal continuity property. Some new results concerning the behavior of
the Lorentzian distance on distinguishing, causally continuous, and causally
simple spacetimes are obtained. Finally, a formula which gives the Lorentzian
distance on the direct product in terms of the distances on the two factors
(M,g) and (H,h) is obtained.Comment: 22 pages, 2 figures, uses the package psfra
Causally simple inextendible spacetimes are hole-free
It is shown that causally simple inextendible spacetimes are hole-free, thus
confirming the expectation that causal simplicity removes holes from spacetime.
This result is optimal in the sense that causal simplicity cannot be weakened
to causal continuity. Physically, it means that if there is some partial Cauchy
hypersurface which, for some reason, does not fully develop its influence, then
there is some discontinuity in the causal relation.Comment: Revtex4, 9 pages. v2: minor correction
Non-imprisonment conditions on spacetime
The non-imprisonment conditions on spacetimes are studied. It is proved that
the non-partial imprisonment property implies the distinction property.
Moreover, it is proved that feeble distinction, a property which stays between
weak distinction and causality, implies non-total imprisonment. As a result the
non-imprisonment conditions can be included in the causal ladder of spacetimes.
Finally, totally imprisoned causal curves are studied in detail, and results
concerning the existence and properties of minimal invariant sets are obtained.Comment: 12 pages, 2 figures. v2: improved results on totally imprisoned
curves, a figure changed, some misprints fixe
Lightlike simultaneity, comoving observers and distances in general relativity
We state a condition for an observer to be comoving with another observer in
general relativity, based on the concept of lightlike simultaneity. Taking into
account this condition, we study relative velocities, Doppler effect and light
aberration. We obtain that comoving observers observe the same light ray with
the same frequency and direction, and so gravitational redshift effect is a
particular case of Doppler effect. We also define a distance between an
observer and the events that it observes, that coincides with the known affine
distance. We show that affine distance is a particular case of radar distance
in the Minkowski space-time and generalizes the proper radial distance in the
Schwarzschild space-time. Finally, we show that affine distance gives us a new
concept of distance in Robertson-Walker space-times, according to Hubble law.Comment: 17 pages, 5 figures. Since "lightlike distance" is in fact the known
"affine distance", the notation has been change
Multiply Warped Products with Non-Smooth Metrics
In this article we study manifolds with -metrics and properties of
Lorentzian multiply warped products. We represent the interior Schwarzschild
space-time as a multiply warped product space-time with warping functions and
we also investigate the curvature of a multiply warped product with
-warping functions. We given the {\it{Ricci curvature}} in terms of ,
for the multiply warped products of the form $M=(0,\
2m)\times_{f_1}R^1\times_{f_2} S^2$.Comment: LaTeX, 7 page
Limit curve theorems in Lorentzian geometry
The subject of limit curve theorems in Lorentzian geometry is reviewed. A
general limit curve theorem is formulated which includes the case of converging
curves with endpoints and the case in which the limit points assigned since the
beginning are one, two or at most denumerable. Some applications are
considered. It is proved that in chronological spacetimes, strong causality is
either everywhere verified or everywhere violated on maximizing lightlike
segments with open domain. As a consequence, if in a chronological spacetime
two distinct lightlike lines intersect each other then strong causality holds
at their points. Finally, it is proved that two distinct components of the
chronology violating set have disjoint closures or there is a lightlike line
passing through each point of the intersection of the corresponding boundaries.Comment: 25 pages, 1 figure. v2: Misprints fixed, matches published versio
Geometric Analysis of Particular Compactly Constructed Time Machine Spacetimes
We formulate the concept of time machine structure for spacetimes exhibiting
a compactely constructed region with closed timelike curves. After reviewing
essential properties of the pseudo Schwarzschild spacetime introduced by A.
Ori, we present an analysis of its geodesics analogous to the one conducted in
the case of the Schwarzschild spacetime. We conclude that the pseudo
Schwarzschild spacetime is geodesically incomplete and not extendible to a
complete spacetime. We then introduce a rotating generalization of the pseudo
Schwarzschild metric, which we call the the pseudo Kerr spacetime. We establish
its time machine structure and analyze its global properties.Comment: 14 pages, 3 figure
Kinematic relative velocity with respect to stationary observers in Schwarzschild spacetime
We study the kinematic relative velocity of general test particles with
respect to stationary observers (using spherical coordinates) in Schwarzschild
spacetime, obtaining that its modulus does not depend on the observer, unlike
Fermi, spectroscopic and astrometric relative velocities. We study some
fundamental particular cases, generalizing some results given in other work
about stationary and radial free-falling test particles. Moreover, we give a
new result about test particles with circular geodesic orbits: the modulus of
their kinematic relative velocity with respect to any stationary observer
depends only on the radius of the circular orbit, and so, it remains constant.Comment: 8 pages, 2 figure
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