704 research outputs found
Modelling gravity on a hyper-cubic lattice
We present an elegant and simple dynamical model of symmetric, non-degenerate
(n x n) matrices of fixed signature defined on a n-dimensional hyper-cubic
lattice with nearest-neighbor interactions. We show how this model is related
to General Relativity, and discuss multiple ways in which it can be useful for
studying gravity, both classical and quantum. In particular, we show that the
dynamics of the model when all matrices are close to the identity corresponds
exactly to a finite-difference discretization of weak-field gravity in harmonic
gauge. We also show that the action which defines the full dynamics of the
model corresponds to the Einstein-Hilbert action to leading order in the
lattice spacing, and use this observation to define a lattice analogue of the
Ricci scalar and Einstein tensor. Finally, we perform a mean-field analysis of
the statistical mechanics of this model.Comment: 5 page
Twilight for the energy conditions?
The tension, if not outright inconsistency, between quantum physics and
general relativity is one of the great problems facing physics at the turn of
the millennium. Most often, the problems arising in merging Einstein gravity
and quantum physics are viewed as Planck scale issues (10^{19} GeV, 10^{-34} m,
10^{-45} s), and so safely beyond the reach of experiment. However, over the
last few years it has become increasingly obvious that the difficulties are
more widespread: There are already serious problems of deep and fundamental
principle at the semi-classical level, and worse, certain classical systems
(inspired by quantum physics, but in no sense quantum themselves) exhibit
seriously pathological behaviour. One manifestation of these pathologies is in
the so-called ``energy conditions'' of general relativity. Patching things up
in the gravity sector opens gaping holes elsewhere; and some ``fixes'' are more
radical than the problems they are supposed to cure.Comment: Honourable mention in the 2002 Gravity Research Foundation essay
contest. 12 pages. Plain LaTeX 2
Supersonic optical tunnels for Bose-Einstein condensates
We propose a method for the stabilisation of a stack of parallel vortex rings
in a Bose-Einstein condensate. The method makes use of a hollow laser beam
containing an optical vortex. Using realistic experimental parameters we
demonstrate numerically that our method can stabilise up to 9 vortex rings.
Furthermore we point out that the condensate flow through the tunnel formed by
the core of the optical vortex can be made supersonic by inserting a
laser-generated hump potential. We show that long-living immobile condensate
solitons generated in the tunnel exhibit sonic horizons. Finally, we discuss
prospects of using these solitons for analogue gravity experiments.Comment: 14 pages, 3 figures, published versio
Dynamical Aspects of Analogue Gravity: The Backreaction of Quantum Fluctuations in Dilute Bose-Einstein Condensates
We discuss the backreaction force exerted by quantum fluctuations in dilute
Bose-Einstein condensates onto the motion of the classical background, derived
by an ab initio approach from microscopic physics. It is shown that the
effective-action method, widely employed in semiclassical quantum gravity,
fails to give the full backreaction force. The failure of the effective-action
method is traced back, inter alia, to the problem of the correct choice of the
fundamental variables and the related operator ordering issues.Comment: 21+epsilon pages; has appeared in Springer Lecture Notes in Physic
Circular strings, wormholes and minimum size
The quantization of circular strings in an anti-de Sitter background
spacetime is performed, obtaining a discrete spectrum for the string mass. A
comparison with a four-dimensional homogeneous and isotropic spacetime coupled
to a conformal scalar field shows that the string radius and the scale factor
have the same classical solutions and that the quantum theories of these two
models are formally equivalent. However, the physically relevant observables of
these two systems have different spectra, although they are related to each
other by a specific one-to-one transformation. We finally obtain a discrete
spectrum for the spacetime size of both systems, which presents a nonvanishing
lower bound.Comment: 11 pages, LaTeX2e, minor change
Traversable Wormholes Construction in 2+1 Dimensions
We study traversable Lorentzian wormholes in the three-dimensional low energy
string theory by adding some matter source involving a dilaton field. It will
be shown that there are two-different types of wormhole solutions such as BTZ
and black string wormholes depending on the dilaton backgrounds, respectively.
We finally obtain the desirable solutions which confine exotic matter near the
throat of wormhole by adjusting NS charge.Comment: 12 pages, 4 figures, JHEP style, one reference adde
Painlev\'e-Gullstrand synchronizations in spherical symmetry
A Painlev\'e-Gullstrand synchronization is a slicing of the space-time by a
family of flat spacelike 3-surfaces. For spherically symmetric space-times, we
show that a Painlev\'e-Gullstrand synchronization only exists in the region
where , being the curvature radius of the isometry group
orbits (-spheres). This condition says that the Misner-Sharp gravitational
energy of these 2-spheres is not negative and has an intrinsic meaning in terms
of the norm of the mean extrinsic curvature vector. It also provides an
algebraic inequality involving the Weyl curvature scalar and the Ricci
eigenvalues. We prove that the energy and momentum densities associated with
the Weinberg complex of a Painlev\'e-Gullstrand slice vanish in these curvature
coordinates, and we give a new interpretation of these slices by using
semi-metric Newtonian connections. It is also outlined that, by solving the
vacuum Einstein's equations in a coordinate system adapted to a
Painlev\'e-Gullstrand synchronization, the Schwarzschild solution is directly
obtained in a whole coordinate domain that includes the horizon and both its
interior and exterior regions.Comment: 16 page
Evolution of transonicity in an accretion disc
For inviscid, rotational accretion flows driven by a general pseudo-Newtonian
potential on to a Schwarzschild black hole, the only possible fixed points are
saddle points and centre-type points. For the specific choice of the Newtonian
potential, the flow has only two critical points, of which the outer one is a
saddle point while the inner one is a centre-type point. A restrictive upper
bound is imposed on the admissible range of values of the angular momentum of
sub-Keplerian flows through a saddle point. These flows are very unstable to
any deviation from a necessarily precise boundary condition. The difficulties
against the physical realisability of a solution passing through the saddle
point have been addressed through a temporal evolution of the flow, which gives
a non-perturbative mechanism for selecting a transonic solution passing through
the saddle point. An equation of motion for a real-time perturbation about the
stationary flows reveals a very close correspondence with the metric of an
acoustic black hole, which is also an indication of the primacy of
transonicity.Comment: 18 page
Perturbations on steady spherical accretion in Schwarzschild geometry
The stationary background flow in the spherically symmetric infall of a
compressible fluid, coupled to the space-time defined by the static
Schwarzschild metric, has been subjected to linearized perturbations. The
perturbative procedure is based on the continuity condition and it shows that
the coupling of the flow with the geometry of space-time brings about greater
stability for the flow, to the extent that the amplitude of the perturbation,
treated as a standing wave, decays in time, as opposed to the amplitude
remaining constant in the Newtonian limit. In qualitative terms this situation
simulates the effect of a dissipative mechanism in the classical Bondi
accretion flow, defined in the Newtonian construct of space and time. As a
result of this approach it becomes impossible to define an acoustic metric for
a conserved spherically symmetric flow, described within the framework of
Schwarzschild geometry. In keeping with this view, the perturbation, considered
separately as a high-frequency travelling wave, also has its amplitude reduced.Comment: 8 pages, no figur
Relationship between bulk phase, near surface and outermost atomic layer of VPO catalysts and their catalytic performance in the oxidative dehydrogenation of ethane
A set of vanadium phosphorous oxide (VPO) catalysts, mainly consisting of (VO)<sub>2</sub>P<sub>2</sub>O<sub>7</sub>, VO(PO<sub>3</sub>)<sub>2</sub> or VOPO<sub>4</sub>∙2H<sub>2</sub>O bulk crystalline phases, has been investigated for the oxidative dehydrogenation (ODH) of ethane to ethylene, a key potential reaction for a sustainable industrial and socioeconomic development. The catalytic performance on these VPO catalysts has been explained on the basis of the main crystalline phases and the corresponding suface features found by XPS and LEISS at 400 ˚C, i.e. within the temperature range used for ODH reaction. The catalysts based on (VO)<sub>2</sub>P<sub>2</sub>O<sub>7</sub> phase presented the highest catalytic activity and productivity to ethylene. Nevertheless, the catalysts consisting of VO(PO<sub>3</sub>)<sub>2</sub> structure showed higher selectivity to ethylene, reaching 90% selectivity at ca. 10% ethane conversion. To the best of our knowledge, this is the highest selectivity reported on a vanadium phosphorous oxide at similar conversions for the ethane ODH. In general, catalysts consisting of crystalline phases with vanadium present as V<sup>4+</sup>, i.e. (VO)<sub>2</sub>P<sub>2</sub>O<sub>7</sub> and VO(PO<sub>3</sub>)<sub>2</sub>, were found to be significantly more selective to ethylene than those containing V<sup>5+</sup> phases. The surface analysis by XPS showed an inverse correlation between the mean oxidation state of vanadium near surface and the selectivity to ethylene. The lower averaged oxidation states of vanadium appear to be favoured by the presence of V<sup>3+</sup> species near the surface, which was only found in the catalysts containing V<sup>4+</sup> phases. Among those catalysts the one based on VO(PO<sub>3</sub>)<sub>2</sub> phase shows the highest selectivity, which could be related to the most isolated scenario of V species (the lowest V content relative to P) found at the outermost surface by low energy ion scattering spectroscopy (LEISS), a "true" surface technique only sensitive to the outermost atomic layer
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