228 research outputs found
Chronology Protection and Non-Naked Singularity
We test the chronology protection conjecture in classical general relativity
by investigating finitely vicious space-times. First we present singularity
theorems in finitely vicious space-times by imposing some restrictions on the
chronology violating sets. In the theorems we can refer to the location of an
occurring singularity and do not assume any asymptotic conditions such as the
existence of null infinities. Further introducing the concept of a non-naked
singularity, we show that a restricted class of chronology violations cannot
arise if all occurring singularities are the non-naked singularities. Our
results suggest that the causal feature of the occurring singularities is the
key to prevent the appearance of causality violation.Comment: 17 pages including 3 eps figures. Accepted for publication in
Classical and Quantum Gravit
Asymptotically Flat Radiating Solutions in Third Order Lovelock Gravity
In this paper, we present an exact spherically symmetric solution of third
order Lovelock gravity in dimensions which describes the gravitational
collapse of a null dust fluid. This solution is asymptotically (anti-)de Sitter
or flat depending on the choice of the cosmological constant. Using the
asymptotically flat solution for with a power-law form of the mass
as a function of the null coordinate, we present a model for a gravitational
collapse in which a null dust fluid radially injects into an initially flat and
empty region. It is found that a naked singularity is inevitably formed whose
strength is different for the and cases. In the case,
the limiting focusing condition for the strength of curvature singularity is
satisfied. But for , the strength of curvature singularity depends on
the rate of increase of mass of the spacetime. These considerations show that
the third order Lovelock term weakens the strength of the curvature
singularity.Comment: 15 pages, no figure, references added, two appendix adde
Initial Conditions for Bubble Universes
The "bubble universes" of Coleman and De Luccia play a crucial role in string
cosmology. Since our own Universe is supposed to be of this kind, bubble
cosmology should supply definite answers to the long-standing questions
regarding cosmological initial conditions. In particular, it must explain how
an initial singularity is avoided, and also how the initial conditions for
Inflation were established. We argue that the simplest non-anthropic approach
to these problems involves a requirement that the spatial sections defined by
distinguished bubble observers should not be allowed to have arbitrarily small
volumes. Casimir energy is a popular candidate for a quantum effect which can
ensure this, but [because it violates energy conditions] there is a danger that
it could lead to non-perturbative instabilities in string theory. We make a
simple proposal for the initial conditions of a bubble universe, and show that
our proposal ensures that the system is non-perturbatively stable. Thus,
low-entropy conditions can be established at the beginning of a bubble universe
without violating the Second Law of thermodynamics and without leading to
instability in string theory. These conditions are inherited from the ambient
spacetime.Comment: Further clarifications; 28 pages including three eps files. This is
the final [accepted for publication] versio
Hawking radiation as tunneling from a Vaidya black hole in noncommutative gravity
In the context of a noncommutative model of coordinate coherent states, we
present a Schwarzschild-like metric for a Vaidya solution instead of the
standard Eddington-Finkelstein metric. This leads to the appearance of an exact
dependent case of the metric. We analyze the resulting metric in
three possible causal structures. In this setup, we find a zero remnant mass in
the long-time limit, i.e. an instable black hole remnant. We also study the
tunneling process across the quantum horizon of such a Vaidya black hole. The
tunneling probability including the time-dependent part is obtained by using
the tunneling method proposed by Parikh and Wilczek in terms of the
noncommutative parameter . After that, we calculate the entropy
associated to this noncommutative black hole solution. However the corrections
are fundamentally trifling; one could respect this as a consequence of quantum
inspection at the level of semiclassical quantum gravity.Comment: 19 pages, 5 figure
Gravitational collapse of homogeneous scalar fields
Conditions under which gravity coupled to self interacting scalar field
determines singularity formation are found and discussed. It is shown that,
under a suitable matching with an external space, the boundary, if collapses
completely, may give rise to a naked singularity. Issues related to the
strength of the singularity are discussed.Comment: LaTeX2e; revised versio
The structure of non-spacelike geodesics in dust collapse
We study here the behaviour of non-spacelike geodesics in dust collapse
models in order to understand the casual structure of the spacetime. The
geodesic families coming out, when the singularity is naked, corresponding to
different initial data are worked out and analyzed. We also bring out the
similarity of the limiting behaviour for different types of geodesics in the
limit of approach to the singularity.Comment: 23 pages, 6 figures, to appear in PR
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
Naked strong curvature singularities in Szekeres space-times
We investigate the occurrence and nature of naked singularities in the
Szekeres space-times. These space-times represent irrotational dust. They do
not have any Killing vectors and they are generalisations of the
Tolman-Bondi-Lemaitre space-times. It is shown that in these space-times there
exist naked singularities that satisfy both the limiting focusing condition and
the strong limiting focusing condition. The implications of this result for the
cosmic censorship hypothesis are discussed.Comment: latex, 9 page
The averaged null energy condition for general quantum field theories in two dimensions
It is shown that the averaged null energy condition is fulfilled for a dense,
translationally invariant set of vector states in any local quantum field
theory in two-dimensional Minkowski spacetime whenever the theory has a mass
gap and possesses an energy-momentum tensor. The latter is assumed to be a
Wightman field which is local relative to the observables, generates locally
the translations, is divergence-free, and energetically bounded. Thus the
averaged null energy condition can be deduced from completely generic, standard
assumptions for general quantum field theory in two-dimensional flat spacetime.Comment: LateX2e, 16 pages, 1 eps figur
Naked Singularities in Spherically Symmetric Inhomogeneous Tolman-Bondi Dust Cloud Collapse
We investigate the occurrence and nature of naked singularity for the
inhomogeneous gravitational collapse of Tolman-Bondi dust clouds.It is shown
that the naked singularities form at the center of the collapsing cloud in a
wide class of collapse models which includes the earlier cases considered by
Eardley and Smarr and Christodoulou. This class also contains self-similar as
well as non-self-similar models. The structure and strength of this singularity
is examined and the question is investigated as to when a non-zero measure set
of non-spacelike trajectories could be emitted from the singularity as opposed
to isolated trajectories coming out. It is seen that the weak energy condition
and positivity of energy density ensures that the families of non-spacelike
trajectories come out of the singularity. The curvature strength of the naked
singularity is examined which provides an important test for its physical
significance and powerful curvature growth near the naked singularity is
pointed out for several subclasses considered. The conditions are discussed for
the naked singularity to be globally naked. Implications for the basic issue of
the final fate of gravitational collapse are considered once the
inhomogeneities in the matter distribution are taken into account. It is argued
that a physical formulation for the cosmic censorship may be evolved which
avoids the features above. Possibilities in this direction are discussed while
indicating that the analysis presented here should be useful for any possible
rigorous formulation of the cosmic censorship hypothesis.Comment: 41 pages, TIFR preprint TAP 9/9
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