8,504 research outputs found
De Sitter Space and Spatial Topology
Morrow-Jones and Witt have shown that generic spatial topologies admit
initial data that evolve to locally de Sitter spacetimes under Einstein's
equations. We simplify their arguments, make them a little more general, and
solve for the global time evolution of the wormhole initial data considered by
them. Finally we give explicit examples of locally de Sitter domains of
development whose universal covers cannot be embedded in de Sitter space.Comment: 21 pages, 7 figure
How the Universe got its Spots
The universe displays a three-dimensional pattern of hot and cold spots in
the radiation remnant from the big bang. The global geometry of the universe
can be revealed in the spatial distribution of these spots. In a topologically
compact universe, distinctive patterns are especially prominent in spatial
correlations of the radiation temperature. Whereas these patterns are usually
washed out in statistical averages, we propose a scheme which uses the
universe's spots to observe global geometry in a manner analogous to the use of
multiple images of a gravitationally lensed quasar to study the geometry of the
lens. To demonstrate how the geometry of space forms patterns in observations
of the microwave sky, we develop a simple real-space approximation to estimate
temperature correlations for any set of cosmological parameters and any global
geometry. We present correlated spheres which clearly show geometric pattern
formation for compact flat universes as well as for the compact negatively
curved space introduced by Weeks and another discovered by Best. These examples
illustrate how future satellite-based observations of the microwave background
can determine the full geometry of the universe.Comment: 16 pages, 26 figure
Weyl Card Diagrams and New S-brane Solutions of Gravity
We construct a new card diagram which accurately draws Weyl spacetimes and
represents their global spacetime structure, singularities, horizons and null
infinity. As examples we systematically discuss properties of a variety of
solutions including black holes as well as recent and new time-dependent
gravity solutions which fall under the S-brane class. The new time-dependent
Weyl solutions include S-dihole universes, infinite arrays and complexified
multi-rod solutions. Among the interesting features of these new solutions is
that they have near horizon scaling limits and describe the decay of unstable
objects.Comment: 78 pages, 32 figures. v2 added referenc
Pair of accelerated black holes in a de Sitter background: the dS C-metric
Following the work of Kinnersley and Walker for flat spacetimes, we have
analyzed the anti-de Sitter C-metric in a previous paper. In the de Sitter
case, Podolsky and Griffiths have established that the de Sitter C-metric (dS
C-metric) found by Plebanski and Demianski describes a pair of accelerated
black holes in the dS background with the acceleration being provided (in
addition to the cosmological constant) by a strut that pushes away the two
black holes or, alternatively, by a string that pulls them. We extend their
analysis mainly in four directions. First, we draw the Carter-Penrose diagrams
of the massless uncharged dS C-metric, of the massive uncharged dS C-metric and
of the massive charged dS C-metric. These diagrams allow us to clearly identify
the presence of two dS black holes and to conclude that they cannot interact
gravitationally. Second, we revisit the embedding of the dS C-metric in the 5D
Minkowski spacetime and we represent the motion of the dS C-metric origin in
the dS 4-hyperboloid as well as the localization of the strut. Third, we
comment on the physical properties of the strut that connects the two black
holes. Finally, we find the range of parameters that correspond to non-extreme
black holes, extreme black holes, and naked particles.Comment: 11 pages, 11 figures (RevTeX4). Published version: references adde
Global properties of warped solutions in General Relativity
Assuming the four-dimensional space-time to be a general warped product of
two surfaces we reduce the four-dimensional Einstein equations to a
two-dimensional problem which can be solved. All global vacuum solutions are
explicitly constructed and analysed. The classification of the solutions
includes the Schwarzschild, the (anti-)de Sitter, and other well-known
solutions but also many exact ones whose detailed global properties to our
knowledge have not been discussed before. They have a natural physical
interpretation describing single or several wormholes, domain walls of
curvature singularities, cosmic strings, cosmic strings surrounded by domain
walls, solutions with closed timelike curves, etc.Comment: 35 pages, 5 eps figures, minor change
Spacetime Embedding Diagrams for Black Holes
We show that the 1+1 dimensional reduction (i.e., the radial plane) of the
Kruskal black hole can be embedded in 2+1 Minkowski spacetime and discuss how
features of this spacetime can be seen from the embedding diagram. The purpose
of this work is educational: The associated embedding diagrams may be useful
for explaining aspects of black holes to students who are familiar with special
relativity, but not general relativity.Comment: 22 pages, 21 figures, RevTex. To be submitted to the American Journal
of Physics. Experts will wish only to skim appendix A and to look at the
pictures. Suggested Maple code is now compatible with MapleV4r
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