5,907 research outputs found
Higher-Dimensional Bulk Wormholes and their Manifestations in Brane Worlds
There is nothing to prevent a higher-dimensional anti-de Sitter bulk
spacetime from containing various other branes in addition to hosting our
universe, presumed to be a positive-tension 3-brane. In particular, it could
contain closed, microscopic branes that form the boundary surfaces of void
bubbles and thus violate the null energy condition in the bulk. The possible
existence of such micro branes can be investigated by considering the
properties of the ground state of a pseudo-Wheeler-DeWitt equation describing
brane quantum dynamics in minisuperspace. If they exist, a concentration of
these micro branes could act as a fluid of exotic matter able to support
macroscopic wormholes connecting otherwise distant regions of the bulk. Were
the brane constituting our universe to expand into a region of the bulk
containing such higher-dimensional macroscopic wormholes, they would likely
manifest themselves in our brane as wormholes of normal dimensionality, whose
spontaneous appearance and general dynamics would seem inexplicably peculiar.
This encounter could also result in the formation of baby universes of a
particular type.Comment: 21 pages, 1 figur
Riemannian geometry of irrotational vortex acoustics
We consider acoustic propagation in an irrotational vortex, using the
technical machinery of differential geometry to investigate the ``acoustic
geometry'' that is probed by the sound waves. The acoustic space-time curvature
of a constant circulation hydrodynamical vortex leads to deflection of phonons
at appreciable distances from the vortex core. The scattering angle for phonon
rays is shown to be quadratic in the small quantity , where
is the vortex circulation, the speed of sound, and the impact
parameter.Comment: 4 pages, 2 figures, RevTex4. Discussion of focal length added; to
appear in Physical Review Letter
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
Inverse hyperbolic problems and optical black holes
In this paper we give a more geometrical formulation of the main theorem in
[E1] on the inverse problem for the second order hyperbolic equation of general
form with coefficients independent of the time variable. We apply this theorem
to the inverse problem for the equation of the propagation of light in a moving
medium (the Gordon equation). Then we study the existence of black and white
holes for the general hyperbolic and for the Gordon equation and we discuss the
impact of this phenomenon on the inverse problems
van Vleck determinants: traversable wormhole spacetimes
Calculating the van Vleck determinant in traversable wormhole spacetimes is
an important ingredient in understanding the physical basis behind Hawking's
chronology protection conjecture. This paper presents extensive computations of
this object --- at least in the short--throat flat--space approximation. An
important technical trick is to use an extension of the usual junction
condition formalism to probe the full Riemann tensor associated with a thin
shell of matter. Implications with regard to Hawking's chronology protection
conjecture are discussed. Indeed, any attempt to transform a single isolated
wormhole into a time machine results in large vacuum polarization effects
sufficient to disrupt the internal structure of the wormhole before the onset
of Planck scale physics, and before the onset of time travel. On the other
hand, it is possible to set up a putative time machine built out of two or more
wormholes, each of which taken in isolation is not itself a time machine. Such
``Roman configurations'' are much more subtle to analyse. For some particularly
bizarre configurations (not traversable by humans) the vacuum polarization
effects can be arranged to be arbitrarily small at the onset of Planck scale
physics. This indicates that the disruption scale has been pushed down into the
Planck slop. Ultimately, for these configurations, questions regarding the
truth or falsity of Hawking's chronology protection can only be addressed by
entering the uncharted wastelands of full fledged quantum gravity.Comment: 42 pages, ReV_TeX 3.
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
Energy conditions in f(R) gravity and Brans-Dicke theories
The equivalence between f(R) gravity and scalar-tensor theories is invoked to
study the null, strong, weak and dominant energy conditions in Brans-Dicke
theory. We consider the validity of the energy conditions in Brans-Dicke theory
by invoking the energy conditions derived from a generic f(R) theory. The
parameters involved are shown to be consistent with an accelerated expanding
universe.Comment: 9 pages, 1 figure, to appear in IJMP
Spacetime geometry of static fluid spheres
We exhibit a simple and explicit formula for the metric of an arbitrary
static spherically symmetric perfect fluid spacetime. This class of metrics
depends on one freely specifiable monotone non-increasing generating function.
We also investigate various regularity conditions, and the constraints they
impose. Because we never make any assumptions as to the nature (or even the
existence) of an equation of state, this technique is useful in situations
where the equation of state is for whatever reason uncertain or unknown.
To illustrate the power of the method we exhibit a new form of the
``Goldman--I'' exact solution and calculate its total mass. This is a
three-parameter closed-form exact solution given in terms of algebraic
combinations of quadratics. It interpolates between (and thereby unifies) at
least six other reasonably well-known exact solutions.Comment: Plain LaTeX 2e -- V2: now 22 pages; minor presentation changes in the
first part of the paper -- no physics modifications; major additions to the
examples section: the Gold-I solution is shown to be identical to the G-G
solution. The interior Schwarzschild, Stewart, Buch5 XIII, de Sitter, anti-de
Sitter, and Einstein solutions are all special cases. V3: Reference,
footnotes, and acknowledgments added, typos fixed -- no physics
modifications. V4: Technical problems with mass formula fixed -- affects
discussion of our examples but not the core of the paper. Version to appear
in Classical and Quantum Gravit
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
Stable gravastars with generalised exteriors
New spherically symmetric gravastar solutions, stable to radial
perturbations, are found by utilising the construction of Visser and Wiltshire.
The solutions possess an anti--de Sitter or de Sitter interior and a
Schwarzschild--(anti)--de Sitter or Reissner--Nordstr\"{o}m exterior. We find a
wide range of parameters which allow stable gravastar solutions, and present
the different qualitative behaviours of the equation of state for these
parameters.Comment: 14 pages, 11 figures, to appear in Classical and Quantum Gravit
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