8,057 research outputs found
The causal structure of spacetime is a parameterized Randers geometry
There is a by now well-established isomorphism between stationary
4-dimensional spacetimes and 3-dimensional purely spatial Randers geometries -
these Randers geometries being a particular case of the more general class of
3-dimensional Finsler geometries. We point out that in stably causal
spacetimes, by using the (time-dependent) ADM decomposition, this result can be
extended to general non-stationary spacetimes - the causal structure (conformal
structure) of the full spacetime is completely encoded in a parameterized
(time-dependent) class of Randers spaces, which can then be used to define a
Fermat principle, and also to reconstruct the null cones and causal structure.Comment: 8 page
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
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
Restrictions on negative energy density in a curved spacetime
Recently a restriction ("quantum inequality-type relation") on the
(renormalized) energy density measured by a static observer in a "globally
static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for
the minimally coupled scalar field, in the extension of quantum inequality-type
relation on flat spacetime of Ford and Roman. They found negative lower bounds
for the line integrals of energy density multiplied by a sampling (weighting)
function, and explicitly evaluate them for some specific spacetimes. In this
paper, we study the lower bound on spacetimes whose spacelike hypersurfaces are
compact and without boundary. In the short "sampling time" limit, the bound has
asymptotic expansion. Although the expansion can not be represented by locally
invariant quantities in general due to the nonlocal nature of the integral, we
explicitly evaluate the dominant terms in the limit in terms of the invariant
quantities. We also make an estimate for the bound in the long sampling time
limit.Comment: LaTex, 23 Page
Might EPR particles communicate through a wormhole?
We consider the two-particle wave function of an Einstein-Podolsky-Rosen
system, given by a two dimensional relativistic scalar field model. The Bohm-de
Broglie interpretation is applied and the quantum potential is viewed as
modifying the Minkowski geometry. In this way an effective metric, which is
analogous to a black hole metric in some limited region, is obtained in one
case and a particular metric with singularities appears in the other case,
opening the possibility, following Holland, of interpreting the EPR
correlations as being originated by an effective wormhole geometry, through
which the physical signals can propagate.Comment: Corrected version, to appears in EP
Fundamental limitations on "warp drive" spacetimes
"Warp drive" spacetimes are useful as "gedanken-experiments" that force us to
confront the foundations of general relativity, and among other things, to
precisely formulate the notion of "superluminal" communication. We verify the
non-perturbative violation of the classical energy conditions of the Alcubierre
and Natario warp drive spacetimes and apply linearized gravity to the
weak-field warp drive, testing the energy conditions to first and second order
of the non-relativistic warp-bubble velocity. We are primarily interested in a
secondary feature of the warp drive that has not previously been remarked upon,
if it could be built, the warp drive would be an example of a "reaction-less
drive". For both the Alcubierre and Natario warp drives we find that the
occurrence of significant energy condition violations is not just a high-speed
effect, but that the violations persist even at arbitrarily low speeds.
An interesting feature of this construction is that it is now meaningful to
place a finite mass spaceship at the center of the warp bubble, and compare the
warp field energy with the mass-energy of the spaceship. There is no hope of
doing this in Alcubierre's original version of the warp-field, since by
definition the point in the center of the warp bubble moves on a geodesic and
is "massless". That is, in Alcubierre's original formalism and in the Natario
formalism the spaceship is always treated as a test particle, while in the
linearized theory we can treat the spaceship as a finite mass object. For both
the Alcubierre and Natario warp drives we find that even at low speeds the net
(negative) energy stored in the warp fields must be a significant fraction of
the mass of the spaceship.Comment: 18 pages, Revtex4. V2: one reference added, some clarifying comments
and discussion, no physics changes, accepted for publication in Classical and
Quantum Gravit
Hawking-like radiation does not require a trapped region
We discuss the issue of quasi-particle production by ``analogue black holes''
with particular attention to the possibility of reproducing Hawking radiation
in a laboratory. By constructing simple geometric acoustic models, we obtain a
somewhat unexpected result: We show that in order to obtain a stationary and
Planckian emission of quasi-particles, it is not necessary to create a trapped
region in the acoustic spacetime (corresponding to a supersonic regime in the
fluid flow). It is sufficient to set up a dynamically changing flow
asymptotically approaching a sonic regime with sufficient rapidity in
laboratory time.Comment: revtex4, 4 pages, 1 figur
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