63 research outputs found
Gauge dependence in the theory of non-linear spacetime perturbations
Diffeomorphism freedom induces a gauge dependence in the theory of spacetime
perturbations. We derive a compact formula for gauge transformations of
perturbations of arbitrary order. To this end, we develop the theory of Taylor
expansions for one-parameter families (not necessarily groups) of
diffeomorphisms. First, we introduce the notion of knight diffeomorphism, that
generalises the usual concept of flow, and prove a Taylor's formula for the
action of a knight on a general tensor field. Then, we show that any
one-parameter family of diffeomorphisms can be approximated by a family of
suitable knights. Since in perturbation theory the gauge freedom is given by a
one-parameter family of diffeomorphisms, the expansion of knights is used to
derive our transformation formula. The problem of gauge dependence is a purely
kinematical one, therefore our treatment is valid not only in general
relativity, but in any spacetime theory.Comment: paper accepted for publication in Communications of Mathematical
Physics; SISSA preprint 105/97/A. 10 pages and 2 figures, standard late
Total quantum state in the Einstein-Podolsky-Rosen-Bohm experiment with identical particles
The spin state in the Einstein-Podolsky-Rosen-Bohm gedankenexperiment with identical particles is supplemented by the spatial part. This allows one to extract all the information needed in a typical EPR argument, without requiring semi-intuitive steps. Local spin operators are introduced, to describe measurements of spin in given regions of space
Unexpectedly large surface gravities for acoustic horizons?
Acoustic black holes are fluid dynamic analogs of general relativistic black
holes, wherein the behaviour of sound waves in a moving fluid acts as an analog
for scalar fields propagating in a gravitational background. Acoustic horizons
possess many of the properties more normally associated with the event horizons
of general relativity, up to and including Hawking radiation. They have
received much attention because it would seem to be much easier to
experimentally create an acoustic horizon than to create an event horizon. We
wish to point out some potential difficulties (and opportunities) in actually
setting up an experiment that possesses an acoustic horizon. We show that in
zero-viscosity, stationary fluid flow with generic boundary conditions, the
creation of an acoustic horizon is accompanied by a formally infinite ``surface
gravity'', and a formally infinite Hawking flux. Only by applying a suitable
non-constant external body force, and for very specific boundary conditions on
the flow, can these quantities be kept finite. This problem is ameliorated in
more realistic models of the fluid. For instance, adding viscosity always makes
the Hawking flux finite, but greatly complicates the behaviour of the acoustic
radiation --- viscosity is tantamount to explicitly breaking ``acoustic Lorentz
invariance''. Thus, this issue represents both a difficulty and an opportunity
--- acoustic horizons may be somewhat more difficult to form than naively
envisaged, but if formed, they may be much easier to detect than one would at
first suppose.Comment: Plain LaTeX2e, 32 pages, 10 encapsulated postscript figures; Revised
in view of referee comments; More discussion, (role of viscosity,
relationship with other models), more references; physics and presentation
clarified but central conclusions unaltere
Optical geometry analysis of the electromagnetic self-force
We present an analysis of the behaviour of the electromagnetic self-force for
charged particles in a conformally static spacetime, interpreting the results
with the help of optical geometry. Some conditions for the vanishing of the
local terms in the self-force are derived and discussed.Comment: 18 pages; 2 figure
Hawking-like radiation from evolving black holes and compact horizonless objects
Usually, Hawking radiation is derived assuming (i) that a future eternal
event horizon forms, and (ii) that the subsequent exterior geometry is static.
However, one may be interested in either considering quasi-black holes (objects
in an ever-lasting state of approach to horizon formation, but never quite
forming one), where (i) fails, or, following the evolution of a black hole
during evaporation, where (ii) fails. We shall verify that as long as one has
an approximately exponential relation between the affine parameters on the null
generators of past and future null infinity, then subject to a suitable
adiabatic condition being satisfied, a Planck-distributed flux of Hawking-like
radiation will occur. This happens both for the case of an evaporating black
hole, as well as for the more dramatic case of a collapsing object for which no
horizon has yet formed (or even will ever form). In this article we shall cast
the previous statement in a more precise and quantitative form, and
subsequently provide several explicit calculations to show how the
time-dependent Bogoliubov coefficients can be calculated.Comment: V1: 34 pages. V2: 35 pages; several additional references added; this
version accepted for publication in JHE
On the Tail Problem in Cosmology
The tail problem for the propagation of a scalar field is considered in a
cosmological background, taking a Robertson-Walker spacetime as a specific
example. The explicit radial dependence of the general solution of the
Klein-Gordon equation with nonminimal coupling is derived, and the
inapplicability of the standard calculation of the reflection and transmission
coefficients to the study of scattering of waves by the cosmological curvature
is discussed.Comment: 12 page
Deriving relativistic momentum and energy. II. Three-dimensional case
We generalise a recent derivation of the relativistic expressions for
momentum and kinetic energy from the one-dimensional to the three-dimensional
case.Comment: 7 page
Quasi-particle creation by analogue black holes
30 pages, 16 figures.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 an ergoregion in the acoustic spacetime (corresponding to a supersonic regime in the flow). It is sufficient to set up a dynamically changing flow either eventually generating an arbitrarily small sonic region v=c, but without any ergoregion, or even just asymptotically, in laboratory time, approaching a sonic regime with sufficient rapidity.C.B. has been funded by the spanish MEC under project FIS2005-05736-C03-01 with a partial FEDER contribution. C.B. and S.L. are also supported by a INFN-MEC
collaboration. The research of M.V. was funded in part by the Marsden Fund administered by the Royal Society of New Zealand.Peer reviewe
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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