9,740 research outputs found
Tolman mass, generalized surface gravity, and entropy bounds
In any static spacetime the quasi-local Tolman mass contained within a volume
can be reduced to a Gauss-like surface integral involving the flux of a
suitably defined generalized surface gravity. By introducing some basic
thermodynamics and invoking the Unruh effect one can then develop elementary
bounds on the quasi-local entropy that are very similar in spirit to the
holographic bound, and closely related to entanglement entropy.Comment: V1: 4 pages. Uses revtex4-1; V2: Three references added; V3: Some
notational changes for clarity; introductory paragraph rewritten; no physics
changes. This version accepted for publication in Physical Review Letter
Cosmological milestones and energy conditions
Until recently, the physically relevant singularities occurring in FRW
cosmologies had traditionally been thought to be limited to the "big bang", and
possibly a "big crunch". However, over the last few years, the zoo of
cosmological singularities considered in the literature has become considerably
more extensive, with "big rips" and "sudden singularities" added to the mix, as
well as renewed interest in non-singular cosmological events such as "bounces"
and "turnarounds". In this talk, we present an extensive catalogue of such
cosmological milestones, both at the kinematical and dynamical level. First,
using generalized power series, purely kinematical definitions of these
cosmological events are provided in terms of the behaviour of the scale factor
a(t). The notion of a "scale-factor singularity" is defined, and its relation
to curvature singularities (polynomial and differential) is explored. Second,
dynamical information is extracted by using the Friedmann equations (without
assuming even the existence of any equation of state) to place constraints on
whether or not the classical energy conditions are satisfied at the
cosmological milestones. Since the classification is extremely general, and
modulo certain technical assumptions complete, the corresponding results are to
a high degree model-independent.Comment: 8 pages, 1 table, conference proceedings for NEB XII conference in
Nafplio, Greec
Bounding the Hubble flow in terms of the w parameter
The last decade has seen increasing efforts to circumscribe and bound the
cosmological Hubble flow in terms of model-independent constraints on the
cosmological fluid - such as, for instance, the classical energy conditions of
general relativity. Quite a bit can certainly be said in this regard, but much
more refined bounds can be obtained by placing more precise constraints (either
theoretical or observational) on the cosmological fluid. In particular, the use
of the w-parameter (w=p/rho) has become increasingly common as a surrogate for
trying to say something about the cosmological equation of state. Herein we
explore the extent to which a constraint on the w-parameter leads to useful and
nontrivial constraints on the Hubble flow, in terms of constraints on density
rho(z), Hubble parameter H(z), density parameter Omega(z), cosmological
distances d(z), and lookback time T(z). In contrast to other partial results in
the literature, we carry out the computations for arbitrary values of the space
curvature k in [-1,0,+1], equivalently for arbitrary Omega_0 <= 1.Comment: 15 page
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
Effective refractive index tensor for weak field gravity
Gravitational lensing in a weak but otherwise arbitrary gravitational field
can be described in terms of a 3 x 3 tensor, the "effective refractive index".
If the sources generating the gravitational field all have small internal
fluxes, stresses, and pressures, then this tensor is automatically isotropic
and the "effective refractive index" is simply a scalar that can be determined
in terms of a classic result involving the Newtonian gravitational potential.
In contrast if anisotropic stresses are ever important then the gravitational
field acts similarly to an anisotropic crystal. We derive simple formulae for
the refractive index tensor, and indicate some situations in which this will be
important.Comment: V1: 8 pages, no figures, uses iopart.cls. V2: 13 pages, no figures.
Significant additions and clarifications. This version to appear in Classical
and Quantum Gravit
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
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.
Analog black holes in flowing dielectrics
We show that a flowing dielectric medium with a linear response to an
external electric field can be used to generate an analog geometry that has
many of the formal properties of a Schwarzschild black hole for light rays, in
spite of birefringence. We also discuss the possibility of generating these
analog black holes in the laboratory.Comment: Revtex4 file, 7 pages, 4 eps figures, a few changes in presentation,
some references added, conclusions unchange
The Hubble series: Convergence properties and redshift variables
In cosmography, cosmokinetics, and cosmology it is quite common to encounter
physical quantities expanded as a Taylor series in the cosmological redshift z.
Perhaps the most well-known exemplar of this phenomenon is the Hubble relation
between distance and redshift. However, we now have considerable high-z data
available, for instance we have supernova data at least back to redshift
z=1.75. This opens up the theoretical question as to whether or not the Hubble
series (or more generally any series expansion based on the z-redshift)
actually converges for large redshift? Based on a combination of mathematical
and physical reasoning, we argue that the radius of convergence of any series
expansion in z is less than or equal to 1, and that z-based expansions must
break down for z>1, corresponding to a universe less than half its current
size.
Furthermore, we shall argue on theoretical grounds for the utility of an
improved parameterization y=z/(1+z). In terms of the y-redshift we again argue
that the radius of convergence of any series expansion in y is less than or
equal to 1, so that y-based expansions are likely to be good all the way back
to the big bang y=1, but that y-based expansions must break down for y<-1, now
corresponding to a universe more than twice its current size.Comment: 15 pages, 2 figures, accepted for publication in Classical and
Quantum Gravit
Back-reaction effects in acoustic black holes
Acoustic black holes are very interesting non-gravitational objects which can
be described by the geometrical formalism of General Relativity. These models
can be useful to experimentally test effects otherwise undetectable, as for
example the Hawking radiation. The back-reaction effects on the background
quantities induced by the analogue Hawking radiation could be the key to
indirectly observe it. We briefly show how this analogy works and derive the
backreaction equations for the linearized quantum fluctuations in the
background of an acoustic black hole. A first order in hbar solution is given
in the near horizon region. It indicates that acoustic black holes, unlike
Schwarzschild ones, get cooler as they radiate phonons. They show remarkable
analogies with near-extremal Reissner-Nordstrom black holes.Comment: 10 pages, 1 figure; Talk given at the conference ``Constrained
Dynamics and Quantum Gravity (QG05)", Cala Gonone (Italy), September 200
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