60 research outputs found
Signature change events: A challenge for quantum gravity?
Within the framework of either Euclidian (functional-integral) quantum
gravity or canonical general relativity the signature of the manifold is a
priori unconstrained. Furthermore, recent developments in the emergent
spacetime programme have led to a physically feasible implementation of
signature change events. This suggests that it is time to revisit the sometimes
controversial topic of signature change in general relativity. Specifically, we
shall focus on the behaviour of a quantum field subjected to a manifold
containing regions of different signature. We emphasise that, regardless of the
underlying classical theory, there are severe problems associated with any
quantum field theory residing on a signature-changing background. (Such as the
production of what is naively an infinite number of particles, with an infinite
energy density.) From the viewpoint of quantum gravity phenomenology, we
discuss possible consequences of an effective Lorentz symmetry breaking scale.
To more fully understand the physics of quantum fields exposed to finite
regions of Euclidean-signature (Riemannian) geometry, we show its similarities
with the quantum barrier penetration problem, and the super-Hubble horizon
modes encountered in cosmology. Finally we raise the question as to whether
signature change transitions could be fully understood and dynamically
generated within (modified) classical general relativity, or whether they
require the knowledge of a full theory of quantum gravity.Comment: 33 pages. 4 figures; V2: 3 references added, no physics changes; V3:
now 24 pages - significantly shortened - argument simplified and more focused
- no physics changes - this version accepted for publication in Classical and
Quantum Gravit
Analogue model of a FRW universe in Bose-Einstein condensates: Application of the classical field method
Analogue models of gravity have been motivated by the possibility of
investigating phenomena not readily accessible in their cosmological
counterparts. In this paper, we investigate the analogue of cosmological
particle creation in a Friedmann-Robertson-Walker universe by numerically
simulating a Bose-Einstein condensate with a time-dependent scattering length.
In particular, we focus on a two-dimensional homogeneous condensate using the
classical field method via the truncated Wigner approximation. We show that for
various forms of the scaling function the particle production is consistent
with the underlying theory in the long wavelength limit. In this context, we
further discuss the implications of modified dispersion relations that arise
from the microscopic theory of a weakly interacting Bose gas.Comment: 26 pages, 8 figure
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
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
Vortex geometry for the equatorial slice of the Kerr black hole
The spacetime geometry on the equatorial slice through a Kerr black hole is
formally equivalent to the geometry felt by phonons entrained in a rotating
fluid vortex. We analyse this situation in some detail: First, we find the most
general ``acoustic geometry'' compatible with the fluid dynamic equations in a
collapsing/expanding perfect-fluid line vortex. Second, we demonstrate that
there is a suitable choice of coordinates on the equatorial slice through a
Kerr black hole that puts it into this vortex form; though it is not possible
to put the entire Kerr spacetime into perfect-fluid ``acoustic'' form. Finally,
we briefly discuss the implications of this formal equivalence; both with
respect to gaining insight into the Kerr spacetime and with respect to possible
vortex-inspired experiments.Comment: V1: 24 pages, 5 figures (some use of colour); V2: 21 pages, 5
figures, uses iopart.cls Changes of style and emphasis, no major changes in
physics conclusions. This version accepted for publication in Classical and
Quantum Gravit
Transmission probabilities and the Miller-Good transformation
Transmission through a potential barrier, and the related issue of particle
production from a parametric resonance, are topics of considerable general
interest in quantum physics. The authors have developed a rather general bound
on quantum transmission probabilities, and recently applied it to bounding the
greybody factors of a Schwarzschild black hole. In the current article we take
a different tack -- we use the Miller-Good transformation (which maps an
initial Schrodinger equation to a final Schrodinger equation for a different
potential) to significantly generalize the previous bound.Comment: 10 pages. V2: Now 15 pages. Significantly expanded with examples and
applications. Matches published versio
Horizon effects with surface waves on moving water
Surface waves on a stationary flow of water are considered, in a linear model
that includes the surface tension of the fluid. The resulting gravity-capillary
waves experience a rich array of horizon effects when propagating against the
flow. In some cases three horizons (points where the group velocity of the wave
reverses) exist for waves with a single laboratory frequency. Some of these
effects are familiar in fluid mechanics under the name of wave blocking, but
other aspects, in particular waves with negative co-moving frequency and the
Hawking effect, were overlooked until surface waves were investigated as
examples of analogue gravity [Sch\"utzhold R and Unruh W G 2002 Phys. Rev. D 66
044019]. A comprehensive presentation of the various horizon effects for
gravity-capillary waves is given, with emphasis on the deep water/short
wavelength case kh>>1 where many analytical results can be derived. A
similarity of the state space of the waves to that of a thermodynamic system is
pointed out.Comment: 30 pages, 15 figures. Minor change
The Basics of Water Waves Theory for Analogue Gravity
This chapter gives an introduction to the connection between the physics of
water waves and analogue gravity. Only a basic knowledge of fluid mechanics is
assumed as a prerequisite.Comment: 36 pages. Lecture Notes for the IX SIGRAV School on "Analogue
Gravity", Como (Italy), May 201
Perturbative instabilities in Horava gravity
We investigate the scalar and tensor perturbations in Horava gravity, with
and without detailed balance, around a flat background. Once both types of
perturbations are taken into account, it is revealed that the theory is plagued
by ghost-like scalar instabilities in the range of parameters which would
render it power-counting renormalizable, that cannot be overcome by simple
tricks such as analytic continuation. Implementing a consistent flow between
the UV and IR limits seems thus more challenging than initially presumed,
regardless of whether the theory approaches General Relativity at low energies
or not. Even in the phenomenologically viable parameter space, the tensor
sector leads to additional potential problems, such as fine-tunings and
super-luminal propagation.Comment: 21 pages, version published at Class. Quant. Gra
Experimentation on Analogue Models
Summary
Analogue models are actual physical setups used to model something else. They are especially useful when what we wish to investigate is difficult to observe or experiment upon due to size or distance in space or time: for example, if the thing we wish to investigate is too large, too far away, takes place on a time scale that is too long, does not yet exist or has ceased to exist. The range and variety of analogue models is too extensive to attempt a survey. In this article, I describe and discuss several different analogue model experiments, the results of those model experiments, and the basis for constructing them and interpreting their results. Examples of analogue models for surface waves in lakes, for earthquakes and volcanoes in geophysics, and for black holes in general relativity, are described, with a focus on examining the bases for claims that these analogues are appropriate analogues of what they are used to investigate. A table showing three different kinds of bases for reasoning using analogue models is provided. Finally, it is shown how the examples in this article counter three common misconceptions about the use of analogue models in physics
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