80 research outputs found
Note About Hamiltonian Formalism of Healthy Extended Horava-Lifshitz Gravity
In this paper we continue the study of the Hamiltonian formalism of the
healthy extended Horava-Lifshitz gravity. We find the constraint structure of
given theory and argue that this is the theory with the second class
constraints. Then we discuss physical consequence of this result. We also apply
the Batalin-Tyutin formalism of the conversion of the system with the second
class constraints to the system with the first class constraints to the case of
the healthy extended Horava-Lifshitz theory. As a result we find new theory of
gravity with structure that is different from the standard formulation of
Horava-Lifshitz gravity or General Relativity.Comment: 17 pages, v.2. references added, v.3. typos corrected, references
adde
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 imprint of the analogue Hawking effect in subcritical flows
We study the propagation of low-frequency shallow water waves on a one-dimensional flow of varying depth. When taking into account dispersive effects, the linear propagation of long-wavelength modes on uneven bottoms excites new solutions of the dispersion relation which possess a much shorter wavelength. The peculiarity is that one of these new solutions has a negative energy. When the flow becomes supercritical, this mode has been shown to be responsible for the (classical) analog of the Hawking effect. For subcritical flows, the production of this mode has been observed numerically and experimentally, but the precise physics governing the scattering remained unclear. In this work, we provide an analytic treatment of this effect in subcritical flows. We analyze the scattering of low-frequency waves using a new perturbative series, derived from a generalization of the Bremmer series. We show that the production of short-wavelength modes is governed by a complex value of the position: a complex turning point. Using this method, we investigate various flow profiles and derive the main characteristics of the induced spectrum
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
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
On the true nature of renormalizability in Horava-Lifshitz gravity
We argue that the true nature of the renormalizability of Horava-Lifshitz
gravity lies in the presence of higher order spatial derivatives and not in the
anisotropic Lifshitz scaling of space and time. We discuss the possibility of
constructing a higher order spatial derivatives model that has the same
renormalization properties of Horava-Lifshitz gravity but that does not make
use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz
symmetry restoration in Horava-Lifshitz-type theories of gravitation is
reviewed.Comment: Latex file in Revtex style, 5 pages, no figures. v2: references
added, version accepted for publication in Foundations of Physic
Rotational superradiant scattering in a vortex flow
When an incident wave scatters off of an obstacle, it is partially reflected and partially transmitted. In theory, if the obstacle is rotating, waves can be amplified in the process, extracting energy from the scatterer. Here we describe in detail the first laboratory detection of this phenomenon, known as superradiance 1, 2, 3, 4. We observed that waves propagating on the surface of water can be amplified after being scattered by a draining vortex. The maximum amplification measured was 14% ± 8%, obtained for 3.70 Hz waves, in a 6.25-cm-deep fluid, consistent with the superradiant scattering caused by rapid rotation. We expect our experimental findings to be relevant to black-hole physics, since shallow water waves scattering on a draining fluid constitute an analogue of a black hole 5, 6, 7, 8, 9, 10, as well as to hydrodynamics, due to the close relation to over-reflection instabilities 11, 12, 13
Lorentz breaking Effective Field Theory and observational tests
Analogue models of gravity have provided an experimentally realizable test
field for our ideas on quantum field theory in curved spacetimes but they have
also inspired the investigation of possible departures from exact Lorentz
invariance at microscopic scales. In this role they have joined, and sometime
anticipated, several quantum gravity models characterized by Lorentz breaking
phenomenology. A crucial difference between these speculations and other ones
associated to quantum gravity scenarios, is the possibility to carry out
observational and experimental tests which have nowadays led to a broad range
of constraints on departures from Lorentz invariance. We shall review here the
effective field theory approach to Lorentz breaking in the matter sector,
present the constraints provided by the available observations and finally
discuss the implications of the persisting uncertainty on the composition of
the ultra high energy cosmic rays for the constraints on the higher order,
analogue gravity inspired, Lorentz violations.Comment: 47 pages, 4 figures. Lecture Notes for the IX SIGRAV School on
"Analogue Gravity", Como (Italy), May 2011. V.3. Typo corrected, references
adde
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
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