40 research outputs found
Rigidly rotating dust solutions depending upon harmonic functions
We write down the relevant field equations for a stationary axially symmetric
rigidly rotating dust source in such a way that the general solution depends
upon the solution of an elliptic equation and upon harmonic functions. Starting
with the dipole Bonnor solution, we built an asymptotically flat solution with
two curvature singularities on the rotational axis with diverging mass. Apart
from the two point singularities on the axis, the metric is regular everywhere.
Finally, we study a non-asymptotically flat solution with NUT charge and a
massless ring singularity, but with a well-defined mass-energy expression.Comment: typos corrected, final version published in Class. Quantum Gra
Axisymmetric Stationary Solutions as Harmonic Maps
We present a method for generating exact solutions of Einstein equations in
vacuum using harmonic maps, when the spacetime possesses two commutating
Killing vectors. This method consists in writing the axisymmetric stationry
Einstein equations in vacuum as a harmonic map which belongs to the group
SL(2,R), and decomposing it in its harmonic "submaps". This method provides a
natural classification of the solutions in classes (Weil's class, Lewis' class
etc).Comment: 17 TeX pages, one table,( CINVESTAV- preprint 12/93
Chronology protection in stationary three-dimensional spacetimes
We study chronology protection in stationary, rotationally symmetric
spacetimes in 2+1 dimensional gravity, focusing especially on the case of
negative cosmological constant. We show that in such spacetimes closed timelike
curves must either exist all the way to the boundary or, alternatively, the
matter stress tensor must violate the null energy condition in the bulk. We
also show that the matter in the closed timelike curve region gives a negative
contribution to the conformal weight from the point of view of the dual
conformal field theory. We illustrate these properties in a class of examples
involving rotating dust in anti-de Sitter space, and comment on the use of the
AdS/CFT correspondence to study chronology protection.Comment: 20 pages. V2: minor corrections, Outlook expanded, references added,
published versio
The Petrov and Kaigorodov-Ozsv\'ath Solutions: Spacetime as a Group Manifold
The Petrov solution (for ) and the Kaigorodov-Ozsv\'ath solution
(for ) provide examples of vacuum solutions of the Einstein
equations with simply-transitive isometry groups. We calculate the boundary
stress-tensor for the Kaigorodov-Ozsv\'ath solution in the context of the
adS/CFT correspondence. By giving a matrix representation of the Killing
algebra of the Petrov solution, we determine left-invariant one-forms on the
group. The algebra is shown to admit a two-parameter family of linear
deformations a special case of which gives the algebra of the
Kaigorodov-Ozsv\'ath solution. By applying the method of non-linear
realisations to both algebras, we obtain a Lagrangian of Finsler type from the
general first-order action in both cases. Interpreting the Petrov solution as
the exterior solution of a rigidly rotating dust cylinder, we discuss the
question of creation of CTCs by spinning up such a cylinder. We show geodesic
completeness of the Petrov and Kaigorodov-Ozsv\'ath solutions and determine the
behaviour of geodesics in these spacetimes. The holonomy groups were shown to
be given by the Lorentz group in both cases.Comment: 25 pages (latex), 3 figures, corrected a few minor error
Holographic Protection of Chronology in Universes of the Godel Type
We analyze the structure of supersymmetric Godel-like cosmological solutions
of string theory. Just as the original four-dimensional Godel universe, these
solutions represent rotating, topologically trivial cosmologies with a
homogeneous metric and closed timelike curves. First we focus on
"phenomenological" aspects of holography, and identify the preferred
holographic screens associated with inertial comoving observers in Godel
universes. We find that holography can serve as a chronology protection agency:
The closed timelike curves are either hidden behind the holographic screen, or
broken by it into causal pieces. In fact, holography in Godel universes has
many features in common with de Sitter space, suggesting that Godel universes
could represent a supersymmetric laboratory for addressing the conceptual
puzzles of de Sitter holography. Then we initiate the investigation of
"microscopic" aspects of holography of Godel universes in string theory. We
show that Godel universes are T-dual to pp-waves, and use this fact to generate
new Godel-like solutions of string and M-theory by T-dualizing known
supersymmetric pp-wave solutions.Comment: 35 pages, 5 figures. v2: typos corrected, references adde
On rigidly rotating perfect fluid cylinders
The gravitational field of a rigidly rotating perfect fluid cylinder with
gamma- law equation of state is found analytically. The solution has two
parameters and is physically realistic for gamma in the interval (1.41,2].
Closed timelike curves always appear at large distances.Comment: 10 pages, Revtex (galley
The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of a Time Machine
We study the propagator of a non-relativistic, non-interacting particle in
any non-relativistic ``time-machine'' spacetime of the type shown in Fig.~1: an
external, flat spacetime in which two spatial regions, at time and
at time , are connected by two temporal wormholes, one leading from
the past side of to t the future side of and the other from the
past side of to the future side of . We express the propagator
explicitly in terms of those for ordinary, flat spacetime and for the two
wormholes; and from that expression we show that the propagator satisfies
completeness and unitarity in the initial and final ``chronal regions''
(regions without closed timelike curves) and its propagation from the initial
region to the final region is unitary. However, within the time machine it
satisfies neither completeness nor unitarity. We also give an alternative proof
of initial-region-to-final-region unitarity based on a conserved current and
Gauss's theorem. This proof can be carried over without change to most any
non-relativistic time-machine spacetime; it is the non-relativistic version of
a theorem by Friedman, Papastamatiou and Simon, which says that for a free
scalar field, quantum mechanical unitarity follows from the fact that the
classical evolution preserves the Klein-Gordon inner product
k-Essence, superluminal propagation, causality and emergent geometry
The k-essence theories admit in general the superluminal propagation of the
perturbations on classical backgrounds. We show that in spite of the
superluminal propagation the causal paradoxes do not arise in these theories
and in this respect they are not less safe than General Relativity.Comment: 34 pages, 5 figure
Wormholes and Ringholes in a Dark-Energy Universe
The effects that the present accelerating expansion of the universe has on
the size and shape of Lorentzian wormholes and ringholes are considered. It is
shown that, quite similarly to how it occurs for inflating wormholes, relative
to the initial embedding-space coordinate system, whereas the shape of the
considered holes is always preserved with time, their size is driven by the
expansion to increase by a factor which is proportional to the scale factor of
the universe. In the case that dark energy is phantom energy, which is not
excluded by present constraints on the dark-energy equation of state, that size
increase with time becomes quite more remarkable, and a rather speculative
scenario is here presented where the big rip can be circumvented by future
advanced civilizations by utilizing sufficiently grown up wormholes and
ringholes as time machines that shortcut the big-rip singularity.Comment: 11 pages, RevTex, to appear in Phys. Rev.
Can the Universe Create Itself?
The question of first-cause has troubled philosophers and cosmologists alike.
Now that it is apparent that our universe began in a Big Bang explosion, the
question of what happened before the Big Bang arises. Inflation seems like a
very promising answer, but as Borde and Vilenkin have shown, the inflationary
state preceding the Big Bang must have had a beginning also. Ultimately, the
difficult question seems to be how to make something out of nothing. This paper
explores the idea that this is the wrong question --- that that is not how the
Universe got here. Instead, we explore the idea of whether there is anything in
the laws of physics that would prevent the Universe from creating itself.
Because spacetimes can be curved and multiply connected, general relativity
allows for the possibility of closed timelike curves (CTCs). Thus, tracing
backwards in time through the original inflationary state we may eventually
encounter a region of CTCs giving no first-cause. This region of CTCs, may well
be over by now (being bounded toward the future by a Cauchy horizon). We
illustrate that such models --- with CTCs --- are not necessarily inconsistent
by demonstrating self-consistent vacuums for Misner space and a multiply
connected de Sitter space in which the renormalized energy-momentum tensor does
not diverge as one approaches the Cauchy horizon and solves Einstein's
equations. We show such a Universe can be classically stable and
self-consistent if and only if the potentials are retarded, giving a natural
explanation of the arrow of time. Some specific scenarios (out of many possible
ones) for this type of model are described. For example: an inflationary
universe gives rise to baby universes, one of which turns out to be itself.
Interestingly, the laws of physics may allow the Universe to be its own mother.Comment: 48 pages, 8 figure