8,304 research outputs found
Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime
Building on a pair of earlier papers, I investigate the various point-wise
and averaged energy conditions for the quantum stress-energy tensor
corresponding to a conformally-coupled massless scalar field in the in the
(1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors
are analytically known, I can get exact results for the Hartle--Hawking,
Boulware, and Unruh vacua. This exactly solvable model serves as a useful
sanity check on my (3+1)-dimensional investigations wherein I had to resort to
a mixture of analytic approximations and numerical techniques. Key results in
(1+1) dimensions are: (1) NEC is satisfied outside the event horizon for the
Hartle--Hawking vacuum, and violated for the Boulware and Unruh vacua. (2) DEC
is violated everywhere in the spacetime (for any quantum state, not just the
standard vacuum states).Comment: 7 pages, ReV_Te
Microsatellite genotyping of apple (Malus Ă— domestica Borkh.) genetic resources in the Netherlands: application in collection management and variety identification
A highly informative set of 16 microsatellite markers was used to fingerprint 695 apple accessions from eight Dutch collections. Among the total sample, 475 different genotypes were distinguished based on multi-locus microsatellite variation, revealing a potential redundancy within the total sample of 32%. The majority of redundancies were found between collections, rather than within collections. No single collection covered the total observed diversity well, as each collection consisted of about 50% of unique accessions. These findings reflected the fact that most collection holders focus on common Dutch varieties, as well as on region-specific diversity. Based on the diversity patterns observed, maintenance of genetic resources by a network of co-operating collection holders, rather than by collecting the total diversity in a single collection appears to be an efficient approach. Comparison of microsatellite and passport data showed that for many accessions the marker data did not provide support for the registered variety names. Verification of accessions showed that discrepancies between passport and molecular data were largely due to documentation and phenotypic determination errors. With the help of the marker data the varietal names of 45 accessions could be corrected. Microsatellite genotyping of apple appears to be an efficient tool in the management of collections and in variety identification. The development of a marker database was considered relevant as a reference instrument in variety identification and as a source of information about thus far unexplored diversity that could be of interest in the development of new apple varietie
A `warp drive' with more reasonable total energy requirements
I show how a minor modification of the Alcubierre geometry can dramatically
improve the total energy requirements for a `warp bubble' that can be used to
transport macroscopic objects. A spacetime is presented for which the total
negative mass needed is of the order of a few solar masses, accompanied by a
comparable amount of positive energy. This puts the warp drive in the mass
scale of large traversable wormholes. The new geometry satisfies the quantum
inequality concerning WEC violations and has the same advantages as the
original Alcubierre spacetime.Comment: 9 pages, 1 figure; error in calculation correcte
Gravitational vacuum polarization IV: Energy conditions in the Unruh vacuum
Building on a series of earlier papers [gr-qc/9604007, gr-qc/9604008,
gr-qc/9604009], I investigate the various point-wise and averaged energy
conditions in the Unruh vacuum. I consider the quantum stress-energy tensor
corresponding to a conformally coupled massless scalar field, work in the
test-field limit, restrict attention to the Schwarzschild geometry, and invoke
a mixture of analytical and numerical techniques. I construct a semi-analytic
model for the stress-energy tensor that globally reproduces all known numerical
results to within 0.8%, and satisfies all known analytic features of the
stress-energy tensor. I show that in the Unruh vacuum (1) all standard
point-wise energy conditions are violated throughout the exterior region--all
the way from spatial infinity down to the event horizon, and (2) the averaged
null energy condition is violated on all outgoing radial null geodesics. In a
pair of appendices I indicate general strategy for constructing semi-analytic
models for the stress-energy tensor in the Hartle-Hawking and Boulware states,
and show that the Page approximation is in a certain sense the minimal ansatz
compatible with general properties of the stress-energy in the Hartle-Hawking
state.Comment: 40 pages; plain LaTeX; uses epsf.sty (ten encapsulated postscript
figures); two tables (table and tabular environments). Should successfully
compile under both LaTeX 209 and the 209 compatibility mode of LaTeX2
Scalar Field Quantum Inequalities in Static Spacetimes
We discuss quantum inequalities for minimally coupled scalar fields in static
spacetimes. These are inequalities which place limits on the magnitude and
duration of negative energy densities. We derive a general expression for the
quantum inequality for a static observer in terms of a Euclidean two-point
function. In a short sampling time limit, the quantum inequality can be written
as the flat space form plus subdominant correction terms dependent upon the
geometric properties of the spacetime. This supports the use of flat space
quantum inequalities to constrain negative energy effects in curved spacetime.
Using the exact Euclidean two-point function method, we develop the quantum
inequalities for perfectly reflecting planar mirrors in flat spacetime. We then
look at the quantum inequalities in static de~Sitter spacetime, Rindler
spacetime and two- and four-dimensional black holes. In the case of a
four-dimensional Schwarzschild black hole, explicit forms of the inequality are
found for static observers near the horizon and at large distances. It is show
that there is a quantum averaged weak energy condition (QAWEC), which states
that the energy density averaged over the entire worldline of a static observer
is bounded below by the vacuum energy of the spacetime. In particular, for an
observer at a fixed radial distance away from a black hole, the QAWEC says that
the averaged energy density can never be less than the Boulware vacuum energy
density.Comment: 27 pages, 2 Encapsulated Postscript figures, uses epsf.tex, typeset
in RevTe
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
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
Tolman wormholes violate the strong energy condition
For an arbitrary Tolman wormhole, unconstrained by symmetry, we shall define
the bounce in terms of a three-dimensional edgeless achronal spacelike
hypersurface of minimal volume. (Zero trace for the extrinsic curvature plus a
"flare-out" condition.) This enables us to severely constrain the geometry of
spacetime at and near the bounce and to derive general theorems regarding
violations of the energy conditions--theorems that do not involve geodesic
averaging but nevertheless apply to situations much more general than the
highly symmetric FRW-based subclass of Tolman wormholes. [For example: even
under the mildest of hypotheses, the strong energy condition (SEC) must be
violated.] Alternatively, one can dispense with the minimal volume condition
and define a generic bounce entirely in terms of the motion of test particles
(future-pointing timelike geodesics), by looking at the expansion of their
timelike geodesic congruences. One re-confirms that the SEC must be violated at
or near the bounce. In contrast, it is easy to arrange for all the other
standard energy conditions to be satisfied.Comment: 8 pages, ReV-TeX 3.
A Superluminal Subway: The Krasnikov Tube
The ``warp drive'' metric recently presented by Alcubierre has the problem
that an observer at the center of the warp bubble is causally separated from
the outer edge of the bubble wall. Hence such an observer can neither create a
warp bubble on demand nor control one once it has been created. In addition,
such a bubble requires negative energy densities. One might hope that
elimination of the first problem might ameliorate the second as well. We
analyze and generalize a metric, originally proposed by Krasnikov for two
spacetime dimensions, which does not suffer from the first difficulty. As a
consequence, the Krasnikov metric has the interesting property that although
the time for a one-way trip to a distant star cannot be shortened, the time for
a round trip, as measured by clocks on Earth, can be made arbitrarily short. In
our four dimensional extension of this metric, a ``tube'' is constructed along
the path of an outbound spaceship, which connects the Earth and the star.
Inside the tube spacetime is flat, but the light cones are opened out so as to
allow superluminal travel in one direction. We show that, although a single
Krasnikov tube does not involve closed timelike curves, a time machine can be
constructed with a system of two non-overlapping tubes. Furthermore, it is
demonstrated that Krasnikov tubes, like warp bubbles and traversable wormholes,
also involve unphysically thin layers of negative energy density, as well as
large total negative energies, and therefore probably cannot be realized in
practice.Comment: 20 pages, LATEX, 5 eps figures, uses \eps
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
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