4,486 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.
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
Signature change events: A challenge for quantum gravity?
Within the framework of either Euclidian (functional-integral) quantum
gravity or canonical general relativity the signature of the manifold is a
priori unconstrained. Furthermore, recent developments in the emergent
spacetime programme have led to a physically feasible implementation of
signature change events. This suggests that it is time to revisit the sometimes
controversial topic of signature change in general relativity. Specifically, we
shall focus on the behaviour of a quantum field subjected to a manifold
containing regions of different signature. We emphasise that, regardless of the
underlying classical theory, there are severe problems associated with any
quantum field theory residing on a signature-changing background. (Such as the
production of what is naively an infinite number of particles, with an infinite
energy density.) From the viewpoint of quantum gravity phenomenology, we
discuss possible consequences of an effective Lorentz symmetry breaking scale.
To more fully understand the physics of quantum fields exposed to finite
regions of Euclidean-signature (Riemannian) geometry, we show its similarities
with the quantum barrier penetration problem, and the super-Hubble horizon
modes encountered in cosmology. Finally we raise the question as to whether
signature change transitions could be fully understood and dynamically
generated within (modified) classical general relativity, or whether they
require the knowledge of a full theory of quantum gravity.Comment: 33 pages. 4 figures; V2: 3 references added, no physics changes; V3:
now 24 pages - significantly shortened - argument simplified and more focused
- no physics changes - this version accepted for publication in Classical and
Quantum Gravit
Hawking radiation without black hole entropy
In this Letter I point out that Hawking radiation is a purely kinematic
effect that is generic to Lorentzian geometries. Hawking radiation arises for
any test field on any Lorentzian geometry containing an event horizon
regardless of whether or not the Lorentzian geometry satisfies the dynamical
Einstein equations of general relativity. On the other hand, the classical laws
of black hole mechanics are intrinsically linked to the Einstein equations of
general relativity (or their perturbative extension into either semiclassical
quantum gravity or string-inspired scenarios). In particular, the laws of black
hole thermodynamics, and the identification of the entropy of a black hole with
its area, are inextricably linked with the dynamical equations satisfied by the
Lorentzian geometry: entropy is proportional to area (plus corrections) if and
only if the dynamical equations are the Einstein equations (plus corrections).
It is quite possible to have Hawking radiation occur in physical situations in
which the laws of black hole mechanics do not apply, and in situations in which
the notion of black hole entropy does not even make any sense. This observation
has important implications for any derivation of black hole entropy that seeks
to deduce black hole entropy from the Hawking radiation.Comment: Uses ReV_TeX 3.0; Five pages in two-column forma
Quantum Dynamics of Lorentzian Spacetime Foam
A simple spacetime wormhole, which evolves classically from zero throat
radius to a maximum value and recontracts, can be regarded as one possible mode
of fluctuation in the microscopic ``spacetime foam'' first suggested by
Wheeler. The dynamics of a particularly simple version of such a wormhole can
be reduced to that of a single quantity, its throat radius; this wormhole thus
provides a ``minisuperspace model'' for a structure in Lorentzian-signature
foam. The classical equation of motion for the wormhole throat is obtained from
the Einstein field equations and a suitable equation of state for the matter at
the throat. Analysis of the quantum behavior of the hole then proceeds from an
action corresponding to that equation of motion. The action obtained simply by
calculating the scalar curvature of the hole spacetime yields a model with
features like those of the relativistic free particle. In particular the
Hamiltonian is nonlocal, and for the wormhole cannot even be given as a
differential operator in closed form. Nonetheless the general solution of the
Schr\"odinger equation for wormhole wave functions, i.e., the wave-function
propagator, can be expressed as a path integral. Too complicated to perform
exactly, this can yet be evaluated via a WKB approximation. The result
indicates that the wormhole, classically stable, is quantum-mechanically
unstable: A Feynman-Kac decomposition of the WKB propagator yields no spectrum
of bound states. Though an initially localized wormhole wave function may
oscillate for many classical expansion/recontraction periods, it must
eventually leak to large radius values. The possibility of such a mode unstable
against growth, combined withComment: 37 pages, 93-
Non-minimal Wu-Yang wormhole
We discuss exact solutions of three-parameter non-minimal Einstein-Yang-Mills
model, which describe the wormholes of a new type. These wormholes are
considered to be supported by SU(2)-symmetric Yang-Mills field, non-minimally
coupled to gravity, the Wu-Yang ansatz for the gauge field being used. We
distinguish between regular solutions, describing traversable non-minimal
Wu-Yang wormholes, and black wormholes possessing one or two event horizons.
The relation between the asymptotic mass of the regular traversable Wu-Yang
wormhole and its throat radius is analysed.Comment: 9 pages, 2 figures, typos corrected, 2 references adde
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
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
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