12,847 research outputs found
Analogue model for quantum gravity phenomenology
So called "analogue models" use condensed matter systems (typically
hydrodynamic) to set up an "effective metric" and to model curved-space quantum
field theory in a physical system where all the microscopic degrees of freedom
are well understood. Known analogue models typically lead to massless minimally
coupled scalar fields. We present an extended "analogue space-time" programme
by investigating a condensed-matter system - in and beyond the hydrodynamic
limit - that is in principle capable of simulating the massive Klein-Gordon
equation in curved spacetime. Since many elementary particles have mass, this
is an essential step in building realistic analogue models, and an essential
first step towards simulating quantum gravity phenomenology. Specifically, we
consider the class of two-component BECs subject to laser-induced transitions
between the components, and we show that this model is an example for Lorentz
invariance violation due to ultraviolet physics. Furthermore our model suggests
constraints on quantum gravity phenomenology in terms of the "naturalness
problem" and "universality issue".Comment: Talk given at 7th Workshop on Quantum Field Theory Under the
Influence of External Conditions (QFEXT 05), Barcelona, Catalonia, Spain, 5-9
Sep 200
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
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
Entropy bounds in terms of the w parameter
In a pair of recent articles [PRL 105 (2010) 041302 - arXiv:1005.1132; JHEP
1103 (2011) 056 - arXiv:1012.2867] two of the current authors have developed an
entropy bound for equilibrium uncollapsed matter using only classical general
relativity, basic thermodynamics, and the Unruh effect. An odd feature of that
bound, S <= A/2, was that the proportionality constant, 1/2, was weaker than
that expected from black hole thermodynamics, 1/4. In the current article we
strengthen the previous results by obtaining a bound involving the (suitably
averaged) w parameter. Simple causality arguments restrict this averaged
parameter to be <= 1. When equality holds, the entropy bound saturates at the
value expected based on black hole thermodynamics. We also add some clarifying
comments regarding the (net) positivity of the chemical potential. Overall, we
find that even in the absence of any black hole region, we can nevertheless get
arbitrarily close to the Bekenstein entropy.Comment: V1: 14 pages. V2: One reference added. V3: This version accepted for
publication in JHE
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
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.
Modelling Planck-scale Lorentz violation via analogue models
Astrophysical tests of Planck-suppressed Lorentz violations had been
extensively studied in recent years and very stringent constraints have been
obtained within the framework of effective field theory. There are however
still some unresolved theoretical issues, in particular regarding the so called
"naturalness problem" - which arises when postulating that Planck-suppressed
Lorentz violations arise only from operators with mass dimension greater than
four in the Lagrangian. In the work presented here we shall try to address this
problem by looking at a condensed-matter analogue of the Lorentz violations
considered in quantum gravity phenomenology. Specifically, we investigate the
class of two-component BECs subject to laser-induced transitions between the
two components, and we show that this model is an example for Lorentz
invariance violation due to ultraviolet physics. We shall show that such a
model can be considered to be an explicit example high-energy Lorentz
violations where the ``naturalness problem'' does not arise.Comment: Talk given at the Fourth Meeting on Constrained Dynamics and Quantum
Gravity (QG05), Cala Gonone (Sardinia, Italy) September 12-16, 200
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