5,411 research outputs found
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.
Sonoluminescence and the QED vacuum
In this talk I shall describe an extension of the quantum-vacuum approach to
sonoluminescence proposed several years ago by J.Schwinger. We shall first
consider a model calculation based on Bogolubov coefficients relating the QED
vacuum in the presence of an expanded bubble to that in the presence of a
collapsed bubble. In this way we shall derive an estimate for the spectrum and
total energy emitted. This latter will be shown to be proportional to the
volume of space over which the refractive index changes, as Schwinger
predicted. After this preliminary check we shall deal with the physical
constraints that any viable dynamical model for SL has to satisfy in order to
fit the experimental data. We shall emphasize the importance of the timescale
of the change in refractive index. This discussion will led us to propose a
somewhat different version of dynamical Casimir effect in which the change in
volume of the bubble is no longer the only source for the change in the
refractive index.Comment: 15 pages, 1 figure, uses sprocl.sty. Talk at the 4th Workshop on
Quantum Field Theory Under the Influence of External Conditions, Leipzig,
14-18 September, 199
Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime
Building on a pair of earlier papers, I investigate the various point-wise
and averaged energy conditions for the quantum stress-energy tensor
corresponding to a conformally-coupled massless scalar field in the in the
(1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors
are analytically known, I can get exact results for the Hartle--Hawking,
Boulware, and Unruh vacua. This exactly solvable model serves as a useful
sanity check on my (3+1)-dimensional investigations wherein I had to resort to
a mixture of analytic approximations and numerical techniques. Key results in
(1+1) dimensions are: (1) NEC is satisfied outside the event horizon for the
Hartle--Hawking vacuum, and violated for the Boulware and Unruh vacua. (2) DEC
is violated everywhere in the spacetime (for any quantum state, not just the
standard vacuum states).Comment: 7 pages, ReV_Te
Wormhole Cosmology and the Horizon Problem
We construct an explicit class of dynamic lorentzian wormholes connecting
Friedmann-Robertson-Walker (FRW) spacetimes. These wormholes can allow two-way
transmission of signals between spatially separated regions of spacetime and
could permit such regions to come into thermal contact. The cosmology of a
network of early Universe wormholes is discussed.Comment: 13 pages, in RevTe
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
Cosmodynamics: Energy conditions, Hubble bounds, density bounds, time and distance bounds
We refine and extend a programme initiated by one of the current authors
[Science 276 (1997) 88; Phys. Rev. D56 (1997) 7578] advocating the use of the
classical energy conditions of general relativity in a cosmological setting to
place very general bounds on various cosmological parameters. We show how the
energy conditions can be used to bound the Hubble parameter H(z), Omega
parameter Omega(z), density rho(z), distance d(z), and lookback time T(z) as
(relatively) simple functions of the redshift z, present-epoch Hubble parameter
H_0, and present-epoch Omega parameter Omega_0. We compare these results with
related observations in the literature, and confront the bounds with the recent
supernova data.Comment: 21 pages, 2 figure
Gravitational vacuum polarization IV: Energy conditions in the Unruh vacuum
Building on a series of earlier papers [gr-qc/9604007, gr-qc/9604008,
gr-qc/9604009], I investigate the various point-wise and averaged energy
conditions in the Unruh vacuum. I consider the quantum stress-energy tensor
corresponding to a conformally coupled massless scalar field, work in the
test-field limit, restrict attention to the Schwarzschild geometry, and invoke
a mixture of analytical and numerical techniques. I construct a semi-analytic
model for the stress-energy tensor that globally reproduces all known numerical
results to within 0.8%, and satisfies all known analytic features of the
stress-energy tensor. I show that in the Unruh vacuum (1) all standard
point-wise energy conditions are violated throughout the exterior region--all
the way from spatial infinity down to the event horizon, and (2) the averaged
null energy condition is violated on all outgoing radial null geodesics. In a
pair of appendices I indicate general strategy for constructing semi-analytic
models for the stress-energy tensor in the Hartle-Hawking and Boulware states,
and show that the Page approximation is in a certain sense the minimal ansatz
compatible with general properties of the stress-energy in the Hartle-Hawking
state.Comment: 40 pages; plain LaTeX; uses epsf.sty (ten encapsulated postscript
figures); two tables (table and tabular environments). Should successfully
compile under both LaTeX 209 and the 209 compatibility mode of LaTeX2
Wormholes and Child Universes
Evidence to the case that classical gravitation provides the clue to make
sense out of quantum gravity is presented. The key observation is the existence
in classical gravitation of child universe solutions or "almost" solutions,
"almost" because of some singularity problems. The difficulties of these child
universe solutions due to their generic singularity problems will be very
likely be cured by quantum effects, just like for example "almost" instanton
solutions are made relevant in gauge theories with breaking of conformal
invariance. Some well motivated modifcations of General Relativity where these
singularity problems are absent even at the classical level are discussed. High
energy density excitations, responsible for UV divergences in quantum field
theories, including quantum gravity, are likely to be the source of child
universes which carry them out of the original space time. This decoupling
could prevent these high UV excitations from having any influence on physical
amplitudes. Child universe production could therefore be responsible for UV
regularization in quantum field theories which take into account
semiclassically gravitational effects. Child universe production in the last
stages of black hole evaporation, the prediction of absence of tranplanckian
primordial perturbations, connection to the minimum length hypothesis and in
particular the connection to the maximal curvature hypothesis are discussed.
Some discussion of superexcited states in the case these states are Kaluza
Klein excitations is carried out. Finally, the posibility of obtaining "string
like" effects from the wormholes associated with the child universes is
discussed.Comment: Talk presented at the IWARA 2009 Conference, Maresias, Brazil,
October 2009, accepted for publication in the proceedings, World Scientific
format, 8 page
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