344 research outputs found
A Comment on Junction and Energy Conditions in Thin Shells
This comment contains a suggestion for a slight modification of Israel's
covariant formulation of junction conditions between two spacetimes, placing
both sides on equal footing with normals having uniquely defined orientations.
The signs of mass energy densities in thin shells at the junction depend not
only on the orientations of the normals and it is useful therefore to discuss
the sign separately. Calculations gain in clarity by not choosing the
orientations in advance. Simple examples illustrate our point and complete
previous classifications of spherical thin shells in spherically symmetric
spacetimes relevant to cosmology.Comment: (Tex file + PS file with a figure) Tex errors were correcte
Maintaining a Wormhole with a Scalar Field
It is well known that it takes matter that violates the averaged weak energy
condition to hold the throat of a wormhole open. The production of such
``exotic'' matter is usually discussed within the context of quantum field
theory. In this paper I show that it is possible to produce the exotic matter
required to hold a wormhole open classically. This is accomplished by coupling
a scalar field to matter that satisfies the weak energy condition. The
energy-momentum tensor of the scalar field and the matter separately satisfy
the weak energy condition, but there exists an interaction energy-momentum
tensor that does not. It is this interaction energy-momentum tensor that allows
the wormhole to be maintained.Comment: 12 pages, LaTe
Lorentzian and signature changing branes
General hypersurface layers are considered in order to describe brane-worlds
and shell cosmologies. No restriction is placed on the causal character of the
hypersurface which may thus have internal changes of signature. Strengthening
the results in our previous letter [1], we confirm that a good, regular and
consistent description of signature change is achieved in these brane/shells
scenarios, while keeping the hypersurface and the bulk completely regular. Our
formalism allows for a unified description of the traditional timelike
branes/shells together with the signature-changing, or pure null, ones. This
allows for a detailed comparison of the results in both situations. An
application to the case of hypersurface layers in static bulks is presented,
leading to the general Robertson-Walker geometry on the layer --with a possible
signature change. Explicit examples on anti de Sitter bulks are then studied.
The permitted behaviours in different settings (-mirror branes,
asymmetric shells, signature-changing branes) are analysed in detail. We show
in particular that (i) in asymmetric shells there is an upper bound for the
energy density, and (ii) that the energy density within the brane vanishes when
approaching a change of signature. The description of a signature change as a
`singularity' seen from within the brane is considered. We also find new
relations between the fundamental constants in the brane/shell, its tension,
and the cosmological and gravitational constants of the bulk, independently of
the existence or not of a change of signature.Comment: 23 pages, 2 figure
van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes
The van Vleck determinant is an ubiquitous object, arising in many physically
interesting situations such as: (1) WKB approximations to quantum time
evolution operators and Green functions. (2) Adiabatic approximations to heat
kernels. (3) One loop approximations to functional integrals. (4) The theory of
caustics in geometrical optics and ultrasonics. (5) The focussing and
defocussing of geodesic flows in Riemannian manifolds. While all of these
topics are interrelated, the present paper is particularly concerned with the
last case and presents extensive theoretical developments that aid in the
computation of the van Vleck determinant associated with geodesic flows in
Lorentzian spacetimes. {\sl A fortiori} these developments have important
implications for the entire array of topics indicated. PACS: 04.20.-q,
04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.Comment: plain LaTeX, 18 page
Effective Action and Thermodynamics of Radiating Shells in General Relativity
An effective action is obtained for the area and mass aspect of a thin shell
of radiating self-gravitating matter. On following a mini-superspace approach,
the geometry of the embedding space-time is not dynamical but fixed to be
either Minkowski or Schwarzschild inside the shell and Vaidya in the external
space filled with radiation. The Euler-Lagrange equations of motion are
discussed and shown to entail the expected invariance of the effective
Lagrangian under time-reparametrization. They are equivalent to the usual
junction equations and suggest a macroscopic quasi-static thermodynamic
description.Comment: LATeX, 20 pages, 2 Fig
Upper bound for entropy in asymptotically de Sitter space-time
We investigate nature of asymptotically de Sitter space-times containing a
black hole. We show that if the matter fields satisfy the dominant energy
condition and the cosmic censorship holds in the considering space-time, the
area of the cosmological event horizon for an observer approaching a future
timelike infinity does not decrease, i.e. the second law is satisfied. We also
show under the same conditions that the total area of the black hole and the
cosmological event horizon, a quarter of which is the total Bekenstein-Hawking
entropy, is less than , where is a cosmological
constant. Physical implications are also discussed.Comment: 9 pages, REVTeX,2 figures; to be published in Phys.Rev.
Quasi-Spherical Light Cones of the Kerr Geometry
Quasi-spherical light cones are lightlike hypersurfaces of the Kerr geometry
that are asymptotic to Minkowski light cones at infinity. We develop the
equations of these surfaces and examine their properties. In particular, we
show that they are free of caustics for all positive values of the Kerr radial
coordinate r. Useful applications include the propagation of high-frequency
waves, the definition of Kruskal-like coordinates for a spinning black hole and
the characteristic initial-value problem.Comment: LaTeX, 14 pages, 2 figure
Classical dynamics and stability of collapsing thick shells of matter
We study the collapse towards the gravitational radius of a macroscopic
spherical thick shell surrounding an inner massive core. This overall
electrically neutral macroshell is composed by many nested delta-like massive
microshells which can bear non-zero electric charge, and a possibly non-zero
cosmological constant is also included. The dynamics of the shells is described
by means of Israel's (Lanczos) junction conditions for singular hypersurfaces
and, adopting a Hartree (mean field) approach, an effective Hamiltonian for the
motion of each microshell is derived which allows to check the stability of the
matter composing the macroshell. We end by briefly commenting on the quantum
effects which may arise from the extension of our classical treatment to the
semiclassical level.Comment: 16 pages in IOP style, 8 figures, accepted for publication in Class.
Quantum Gra
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.
Self-Screening Hawking Atmosphere in the Presence of a Bulk Viscosity
The recent theory of 't Hooft [ Nucl. Phys. Suppl. {\bf 68}, 174 (1998)]
models the black hole as a system endowed with an envelope of matter that obeys
an equation of state in the form , and acts as a source in
Einstein's equations. The present paper generalizes the 't Hooft theory so as
to take into account a bulk viscosity in the fluid. It is shown that
even a slight positive value of will suffice to yield complete
agreement with the Hawking formula for the entropy of the black hole, if the
value of the constant takes a value that is slightly less than 4/3.
The value corresponds to a radiation fluid.Comment: 12 pages, LaTeX, no figures, minor extensions of the discussion. To
appear in PR
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