11,705 research outputs found
Theorems on gravitational time delay and related issues
Two theorems related to gravitational time delay are proven. Both theorems
apply to spacetimes satisfying the null energy condition and the null generic
condition. The first theorem states that if the spacetime is null geodesically
complete, then given any compact set , there exists another compact set
such that for any , if there exists a ``fastest null
geodesic'', , between and , then cannot enter . As
an application of this theorem, we show that if, in addition, the spacetime is
globally hyperbolic with a compact Cauchy surface, then any observer at
sufficiently late times cannot have a particle horizon. The second theorem
states that if a timelike conformal boundary can be attached to the spacetime
such that the spacetime with boundary satisfies strong causality as well as a
compactness condition, then any ``fastest null geodesic'' connecting two points
on the boundary must lie entirely within the boundary. It follows from this
theorem that generic perturbations of anti-de Sitter spacetime always produce a
time delay relative to anti-de Sitter spacetime itself.Comment: 15 pages, 1 figure. Example of gauge perturbation changed/corrected.
Two footnotes added and one footnote remove
Warped space-time for phonons moving in a perfect nonrelativistic fluid
We construct a kinematical analogue of superluminal travel in the ``warped''
space-times curved by gravitation, in the form of ``super-phononic'' travel in
the effective space-times of perfect nonrelativistic fluids. These warp-field
space-times are most easily generated by considering a solid object that is
placed as an obstruction in an otherwise uniform flow. No violation of any
condition on the positivity of energy is necessary, because the effective
curved space-times for the phonons are ruled by the Euler and continuity
equations, and not by the Einstein field equations.Comment: 7 pages, 1 figure. Version as published; references update
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
A Theoretical Construction of Thin Shell Wormhole from Tidal Charged Black hole
Recently, Dadhich et al [ Phys.Lett.B 487, 1 (2000)] have discovered a black
hole solution localized on a three brane in five dimensional gravity in the
Randall-Sundrum scenario. In this article, we develop a new class of thin shell
wormhole by surgically grafting above two black hole spacetimes. Various
aspects of this thin wormhole are also analyzed.Comment: 14 pages, 6 figures, Accepted in Gen.Rel.Gra
Riemannian geometry of irrotational vortex acoustics
We consider acoustic propagation in an irrotational vortex, using the
technical machinery of differential geometry to investigate the ``acoustic
geometry'' that is probed by the sound waves. The acoustic space-time curvature
of a constant circulation hydrodynamical vortex leads to deflection of phonons
at appreciable distances from the vortex core. The scattering angle for phonon
rays is shown to be quadratic in the small quantity , where
is the vortex circulation, the speed of sound, and the impact
parameter.Comment: 4 pages, 2 figures, RevTex4. Discussion of focal length added; to
appear in Physical Review Letter
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
Wormholes and Child Universes
Evidence to the case that classical gravitation provides the clue to make
sense out of quantum gravity is presented. The key observation is the existence
in classical gravitation of child universe solutions or "almost" solutions,
"almost" because of some singularity problems. The difficulties of these child
universe solutions due to their generic singularity problems will be very
likely be cured by quantum effects, just like for example "almost" instanton
solutions are made relevant in gauge theories with breaking of conformal
invariance. Some well motivated modifcations of General Relativity where these
singularity problems are absent even at the classical level are discussed. High
energy density excitations, responsible for UV divergences in quantum field
theories, including quantum gravity, are likely to be the source of child
universes which carry them out of the original space time. This decoupling
could prevent these high UV excitations from having any influence on physical
amplitudes. Child universe production could therefore be responsible for UV
regularization in quantum field theories which take into account
semiclassically gravitational effects. Child universe production in the last
stages of black hole evaporation, the prediction of absence of tranplanckian
primordial perturbations, connection to the minimum length hypothesis and in
particular the connection to the maximal curvature hypothesis are discussed.
Some discussion of superexcited states in the case these states are Kaluza
Klein excitations is carried out. Finally, the posibility of obtaining "string
like" effects from the wormholes associated with the child universes is
discussed.Comment: Talk presented at the IWARA 2009 Conference, Maresias, Brazil,
October 2009, accepted for publication in the proceedings, World Scientific
format, 8 page
Energy management of three-dimensional minimum-time intercept
A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission
Acoustic horizons for axially and spherically symmetric fluid flow
We investigate the formation of acoustic horizons for an inviscid fluid
moving in a pipe in the case of stationary and axi-symmetric flow. We show
that, differently from what is generally believed, the acoustic horizon forms
in correspondence of either a local minimum or maximum of the flux tube
cross-section. Similarly, the external potential is required to have either a
maximum or a minimum at the horizon, so that the external force has to vanish
there. Choosing a power-law equation of state for the fluid, , we solve the equations of the fluid dynamics and show that the two
possibilities are realized respectively for and . These results
are extended also to the case of spherically symmetric flow.Comment: 6 pages, 3 figure
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