5,530 research outputs found
Area products for stationary black hole horizons
Area products for multi-horizon stationary black holes often have intriguing
properties, and are often (though not always) independent of the mass of the
black hole itself (depending only on various charges, angular momenta, and
moduli). Such products are often formulated in terms of the areas of inner
(Cauchy) horizons and outer (event) horizons, and sometimes include the effects
of unphysical "virtual" horizons. But the conjectured mass-independence
sometimes fails. Specifically, for the Schwarzschild-de Sitter [Kottler] black
hole in (3+1) dimensions it is shown by explicit exact calculation that the
product of event horizon area and cosmological horizon area is not mass
independent. (Including the effect of the third "virtual" horizon does not
improve the situation.) Similarly, in the Reissner-Nordstrom-anti-de Sitter
black hole in (3+1) dimensions the product of inner (Cauchy) horizon area and
event horizon area is calculated (perturbatively), and is shown to be not mass
independent. That is, the mass-independence of the product of physical horizon
areas is not generic. In spherical symmetry, whenever the quasi-local mass m(r)
is a Laurent polynomial in aerial radius, r=sqrt{A/4\pi}, there are
significantly more complicated mass-independent quantities, the elementary
symmetric polynomials built up from the complete set of horizon radii (physical
and virtual). Sometimes it is possible to eliminate the unphysical virtual
horizons, constructing combinations of physical horizon areas that are mass
independent, but they tend to be considerably more complicated than the simple
products and related constructions currently being mooted in the literature.Comment: V1: 16 pages; V2: 9 pages (now formatted in PRD style). Minor change
in title. Extra introduction, background, discussion. Several additional
references; other references updated. Minor typos fixed. This version
accepted for publication in PRD; V3: Minor typos fixed. Published versio
Lovelock Thin-Shell Wormholes
We construct the asymptotically flat charged thin-shell wormholes of Lovelock
gravity in seven dimensions by cut-and-paste technique, and apply the
generalized junction conditions in order to calculate the energy-momentum
tensor of these wormholes on the shell. We find that for negative second order
and positive third order Lovelock coefficients, there are thin-shell wormholes
that respect the weak energy condition. In this case, the amount of normal
matter decreases as the third order Lovelock coefficient increases. For
positive second and third order Lovelock coefficients, the weak energy
condition is violated and the amount of exotic matter decreases as the charge
increases. Finally, we perform a linear stability analysis against a symmetry
preserving perturbation, and find that the wormholes are stable provided the
derivative of surface pressure density with respect to surface energy density
is negative and the throat radius is chosen suitable.Comment: 13 pages, 6 figure
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
Sensitivity of Hawking radiation to superluminal dispersion relations
We analyze the Hawking radiation process due to collapsing configurations in
the presence of superluminal modifications of the dispersion relation. With
such superluminal dispersion relations, the horizon effectively becomes a
frequency-dependent concept. In particular, at every moment of the collapse,
there is a critical frequency above which no horizon is experienced. We show
that, as a consequence, the late-time radiation suffers strong modifications,
both quantitative and qualitative, compared to the standard Hawking picture.
Concretely, we show that the radiation spectrum becomes dependent on the
measuring time, on the surface gravities associated with different frequencies,
and on the critical frequency. Even if the critical frequency is well above the
Planck scale, important modifications still show up.Comment: 14 pages, 7 figures. Extensive paragraph added in conclusions to
clarify obtained result
The vacuum state of quantum gravity contains large virtual masses
In the functional integral approach to quantum gravity, the quantum
configurations are usually treated to order hbar through a stationary phase
approximation around the saddle point of the action where spacetime is flat. We
show that from this point a "level line" in functional space departs, which
comprises a family of static non-flat metrics with zero scalar curvature,
depending on a continuous mass parameter. Furthermore, each of these metrics
can be perturbed by an arbitrary function in such a way to still satisfy the
condition Int(gR)d4x=0. We thus find a set of zero-modes of the gravitational
action which has non-vanishing measure in the functional space. These metrics
will contribute to the functional integral as vacuum fluctuations, on the same
footing as those near the saddle point.Comment: 13 pages, 4 figures; to appear in Class. Q. Gravit
Dirty black holes: Entropy versus area
Considerable interest has recently been expressed in the entropy versus area
relationship for ``dirty'' black holes --- black holes in interaction with
various classical matter fields, distorted by higher derivative gravity, or
infested with various forms of quantum hair. In many cases it is found that the
entropy is simply related to the area of the event horizon: S = k
A_H/(4\ell_P^2). For example, the ``entropy = (1/4) area'' law *holds* for:
Schwarzschild, Reissner--Nordstrom, Kerr--Newman, and dilatonic black holes. On
the other hand, the ``entropy = (1/4) area'' law *fails* for: various types of
(Riemann)^n gravity, Lovelock gravity, and various versions of quantum hair.
The pattern underlying these results is less than clear. This paper
systematizes these results by deriving a general formula for the entropy: S =
{k A_H/(4\ell_P^2)}
+ {1/T_H} \int_\Sigma [rho - {L}_E ] K^\mu d\Sigma_\mu
+ \int_\Sigma s V^\mu d\Sigma_\mu. (K^\mu is the timelike Killing vector,
V^\mu the four velocity of a co--rotating observer.) If no hair is present the
validity of the ``entropy = (1/4) area'' law reduces to the question of whether
or not the Lorentzian energy density for the system under consideration is
formally equal to the Euclideanized Lagrangian. ****** To appear in Physical
Review D 15 July 1993 ****** [Stylistic changes, minor typos fixed, references
updated, discussion of the Born-Infeld system excised]Comment: plain LaTeX, 17 pages, minor revision
Causal structure of acoustic spacetimes
The so-called ``analogue models of general relativity'' provide a number of
specific physical systems, well outside the traditional realm of general
relativity, that nevertheless are well-described by the differential geometry
of curved spacetime. Specifically, the propagation of acoustic disturbances in
moving fluids are described by ``effective metrics'' that carry with them
notions of ``causal structure'' as determined by an exchange of sound signals.
These acoustic causal structures serve as specific examples of what can be done
in the presence of a Lorentzian metric without having recourse to the Einstein
equations of general relativity. (After all, the underlying fluid mechanics is
governed by the equations of traditional hydrodynamics, not by the Einstein
equations.) In this article we take a careful look at what can be said about
the causal structure of acoustic spacetimes, focusing on those containing sonic
points or horizons, both with a view to seeing what is different from standard
general relativity, and to seeing what the similarities might be.Comment: 51 pages, 39 figures (23 colour figures, colour used to convey
physics information.) V2: Two references added, some additional discussion of
maximal analytic extension, plus minor cosmetic change
Analog gravity from field theory normal modes?
We demonstrate that the emergence of a curved spacetime ``effective
Lorentzian geometry'' is a common and generic result of linearizing a field
theory around some non-trivial background. This investigation is motivated by
considering the large number of ``analog models'' of general relativity that
have recently been developed based on condensed matter physics, and asking
whether there is something more fundamental going on. Indeed, linearization of
a classical field theory (a field theoretic ``normal mode analysis'') results
in fluctuations whose propagation is governed by a Lorentzian-signature curved
spacetime ``effective metric''. For a single scalar field, this procedure
results in a unique effective metric, which is quite sufficient for simulating
kinematic aspects of general relativity (up to and including Hawking
radiation). Quantizing the linearized fluctuations, the one-loop effective
action contains a term proportional to the Einstein--Hilbert action, suggesting
that while classical physics is responsible for generating an ``effective
geometry'', quantum physics can be argued to induce an ``effective dynamics''.
The situation is strongly reminiscent of Sakharov's ``induced gravity''
scenario, and suggests that Einstein gravity is an emergent low-energy
long-distance phenomenon that is insensitive to the details of the high-energy
short-distance physics. (We mean this in the same sense that hydrodynamics is a
long-distance emergent phenomenon, many of whose predictions are insensitive to
the short-distance cutoff implicit in molecular dynamics.)Comment: Revtex 4 (beta 5); 12 pages in single-column forma
Evolution of thin-wall configurations of texture matter
We consider the free matter of global textures within the framework of the
perfect fluid approximation in general relativity. We examine thermodynamical
properties of texture matter in comparison with radiation fluid and bubble
matter. Then we study dynamics of thin-wall selfgravitating texture objects,
and show that classical motion can be elliptical (finite), parabolical or
hyperbolical. It is shown that total gravitational mass of neutral textures in
equilibrium equals to zero as was expected. Finally, we perform the
Wheeler-DeWitt's minisuperspace quantization of the theory, obtain exact wave
functions and discrete spectra of bound states with provision for spatial
topology.Comment: intermediate research on nature of dual-radiation matter; LaTeX, 12
pages, 1 figure and epsfig style file included; slightly shortened version
was published in December issue of GR
Might some gamma ray bursts be an observable signature of natural wormholes?
The extragalactic microlensing scenario for natural wormholes is examined. It
is shown that the main features of wormhole lensing events upon the light of
distant Active Galactic Nuclei (AGNs) are similar to some types of already
observed Gamma Ray Bursts (GRBs). Using recent satellite data on GRBs, an upper
limit to the negative mass density -- g cm --
under the form of wormhole-like objects is presented.Comment: extended version, additions on GRB physics, background sources and
cosmological consequences. Two ps figures. Accpeted for publication in Phys.
Rev.
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