8,986 research outputs found
Closed timelike curves in general relativity
Many solutions of Einstein's field equations contain closed timelike curves
(CTC). Some of these solutions refer to ordinary materials in situations which
might occur in the laboratory, or in astrophysics. It is argued that, in
default of a reasonable interpretation of CTC, general relativity does not give
a satisfactory account of all phenomena within its terms of reference.Comment: 3 pages, PACS: 042
Lookback time bounds from energy conditions
In general relativity, the energy conditions are invoked to restrict general
energy-momentum tensors on physical grounds. We show that in the standard
Friedmann-Lemaitre-Robertson-Walker (FLRW) approach to cosmological modeling,
where the energy and matter components of the cosmic fluid are unknown, the
energy conditions provide model-independent bounds on the behavior of the
lookback time of cosmic sources as a function of the redshift for any value of
the spatial curvature. We also confront such bounds with a lookback time sample
which is built from the age estimates of 32 galaxies lying in the interval
and by assuming the total expanding age of the
Universe to be Gyr, as obtained from current cosmic microwave
background experiments. In agreement with previous results, we show that all
energy conditions seem to have been violated at some point of the recent past
of cosmic evolution.Comment: 7 pages, 3 figures. v2: Minor changes, published in Phys.Rev.D in the
present for
Energy Conditions and Cosmic Acceleration
In general relativity, the energy conditions are invoked to restrict general
energy-momentum tensors in different frameworks, and to derive
general results that hold in a variety of general contexts on physical grounds.
We show that in the standard Friedmann-Lemaitre-Robertson-Walker (FLRW)
approach, where the equation of state of the cosmological fluid is unknown, the
energy conditions provide model-independent bounds on the behavior of the
distance modulus of cosmic sources as a function of the redshift for any
spatial curvature. We use the most recent type Ia supernovae (SNe Ia)
observations, which include the new Hubble Space Telescope SNe Ia events, to
carry out a model-independent analysis of the energy conditions violation in
the context of the standard cosmology. We show that both the null (NEC), weak
(WEC) and dominant (DEC) conditions, which are associated with the existence of
the so-called phantom fields, seem to have been violated only recently (), whereas the condition for attractive gravity, i.e., the strong
energy condition (SEC) was firstly violated billions of years ago, at .Comment: 6 pages, 3 figures. v2: References added, misprints corrected,
published in Phys.Rev.D in the present for
Geometric structure of the generic static traversable wormhole throat
Traversable wormholes have traditionally been viewed as intrinsically
topological entities in some multiply connected spacetime. Here, we show that
topology is too limited a tool to accurately characterize a generic traversable
wormhole: in general one needs geometric information to detect the presence of
a wormhole, or more precisely to locate the wormhole throat. For an arbitrary
static spacetime we shall define the wormhole throat in terms of a
2-dimensional constant-time hypersurface of minimal area. (Zero trace for the
extrinsic curvature plus a "flare-out" condition.) This enables us to severely
constrain the geometry of spacetime at the wormhole throat and to derive
generalized theorems regarding violations of the energy conditions-theorems
that do not involve geodesic averaging but nevertheless apply to situations
much more general than the spherically symmetric Morris-Thorne traversable
wormhole. [For example: the null energy condition (NEC), when suitably weighted
and integrated over the wormhole throat, must be violated.] The major technical
limitation of the current approach is that we work in a static spacetime-this
is already a quite rich and complicated system.Comment: 25 pages; plain LaTeX; uses epsf.sty (four encapsulated postscript
figures
Is Quantum Spacetime Foam Unstable?
A very simple wormhole geometry is considered as a model of a mode of
topological fluctutation in Planck-scale spacetime foam. Quantum dynamics of
the hole reduces to quantum mechanics of one variable, throat radius, and
admits a WKB analysis. The hole is quantum-mechanically unstable: It has no
bound states. Wormhole wave functions must eventually leak to large radii. This
suggests that stability considerations along these lines may place strong
constraints on the nature and even the existence of spacetime foam.Comment: 15 page
From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture
The recent interest in ``time machines'' has been largely fueled by the
apparent ease with which such systems may be formed in general relativity,
given relatively benign initial conditions such as the existence of traversable
wormholes or of infinite cosmic strings. This rather disturbing state of
affairs has led Hawking to formulate his Chronology Protection Conjecture,
whereby the formation of ``time machines'' is forbidden. This paper will use
several simple examples to argue that the universe appears to exhibit a
``defense in depth'' strategy in this regard. For appropriate parameter regimes
Casimir effects, wormhole disruption effects, and gravitational back reaction
effects all contribute to the fight against time travel. Particular attention
is paid to the role of the quantum gravity cutoff. For the class of model
problems considered it is shown that the gravitational back reaction becomes
large before the Planck scale quantum gravity cutoff is reached, thus
supporting Hawking's conjecture.Comment: 43 pages,ReV_TeX,major revision
Cosmological milestones and energy conditions
Until recently, the physically relevant singularities occurring in FRW
cosmologies had traditionally been thought to be limited to the "big bang", and
possibly a "big crunch". However, over the last few years, the zoo of
cosmological singularities considered in the literature has become considerably
more extensive, with "big rips" and "sudden singularities" added to the mix, as
well as renewed interest in non-singular cosmological events such as "bounces"
and "turnarounds". In this talk, we present an extensive catalogue of such
cosmological milestones, both at the kinematical and dynamical level. First,
using generalized power series, purely kinematical definitions of these
cosmological events are provided in terms of the behaviour of the scale factor
a(t). The notion of a "scale-factor singularity" is defined, and its relation
to curvature singularities (polynomial and differential) is explored. Second,
dynamical information is extracted by using the Friedmann equations (without
assuming even the existence of any equation of state) to place constraints on
whether or not the classical energy conditions are satisfied at the
cosmological milestones. Since the classification is extremely general, and
modulo certain technical assumptions complete, the corresponding results are to
a high degree model-independent.Comment: 8 pages, 1 table, conference proceedings for NEB XII conference in
Nafplio, Greec
The Hubble series: Convergence properties and redshift variables
In cosmography, cosmokinetics, and cosmology it is quite common to encounter
physical quantities expanded as a Taylor series in the cosmological redshift z.
Perhaps the most well-known exemplar of this phenomenon is the Hubble relation
between distance and redshift. However, we now have considerable high-z data
available, for instance we have supernova data at least back to redshift
z=1.75. This opens up the theoretical question as to whether or not the Hubble
series (or more generally any series expansion based on the z-redshift)
actually converges for large redshift? Based on a combination of mathematical
and physical reasoning, we argue that the radius of convergence of any series
expansion in z is less than or equal to 1, and that z-based expansions must
break down for z>1, corresponding to a universe less than half its current
size.
Furthermore, we shall argue on theoretical grounds for the utility of an
improved parameterization y=z/(1+z). In terms of the y-redshift we again argue
that the radius of convergence of any series expansion in y is less than or
equal to 1, so that y-based expansions are likely to be good all the way back
to the big bang y=1, but that y-based expansions must break down for y<-1, now
corresponding to a universe more than twice its current size.Comment: 15 pages, 2 figures, accepted for publication in Classical and
Quantum Gravit
Tolman wormholes violate the strong energy condition
For an arbitrary Tolman wormhole, unconstrained by symmetry, we shall define
the bounce in terms of a three-dimensional edgeless achronal spacelike
hypersurface of minimal volume. (Zero trace for the extrinsic curvature plus a
"flare-out" condition.) This enables us to severely constrain the geometry of
spacetime at and near the bounce and to derive general theorems regarding
violations of the energy conditions--theorems that do not involve geodesic
averaging but nevertheless apply to situations much more general than the
highly symmetric FRW-based subclass of Tolman wormholes. [For example: even
under the mildest of hypotheses, the strong energy condition (SEC) must be
violated.] Alternatively, one can dispense with the minimal volume condition
and define a generic bounce entirely in terms of the motion of test particles
(future-pointing timelike geodesics), by looking at the expansion of their
timelike geodesic congruences. One re-confirms that the SEC must be violated at
or near the bounce. In contrast, it is easy to arrange for all the other
standard energy conditions to be satisfied.Comment: 8 pages, ReV-TeX 3.
Energy Conditions and Supernovae Observations
In general relativity, the energy conditions are invoked to restrict general
energy-momentum tensors on physical grounds. We show that in the standard
Friedmann-Lemaitre-Robertson-Walker approach to cosmological modelling where
the equation of state of the cosmological fluid is unknown, the energy
conditions provide model-independent bounds on the behavior of the distance
modulus of cosmic sources as a function of the redshift. We use both the gold
and the legacy samples of current type Ia supenovae to carry out a
model-independent analysis of the energy conditions violation in the context of
standard cosmology.Comment: 4 pages, 2 figures; v2: References added, misprints corrected,
published in Phys.Rev.D in the present for
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