31,018 research outputs found
Bounds on negative energy densities in flat spacetime
We generalise results of Ford and Roman which place lower bounds -- known as
quantum inequalities -- on the renormalised energy density of a quantum field
averaged against a choice of sampling function. Ford and Roman derived their
results for a specific non-compactly supported sampling function; here we use a
different argument to obtain quantum inequalities for a class of smooth, even
and non-negative sampling functions which are either compactly supported or
decay rapidly at infinity. Our results hold in -dimensional Minkowski space
() for the free real scalar field of mass . We discuss various
features of our bounds in 2 and 4 dimensions. In particular, for massless field
theory in 2-dimensional Minkowski space, we show that our quantum inequality is
weaker than Flanagan's optimal bound by a factor of 3/2.Comment: REVTeX, 13 pages and 2 figures. Minor typos corrected, one reference
adde
Semiclassical Gravity Theory and Quantum Fluctuations
We discuss the limits of validity of the semiclassical theory of gravity in
which a classical metric is coupled to the expectation value of the stress
tensor. It is argued that this theory is a good approximation only when the
fluctuations in the stress tensor are small. We calculate a dimensionless
measure of these fluctuations for a scalar field on a flat background in
particular cases, including squeezed states and the Casimir vacuum state. It is
found that the fluctuations are small for states which are close to a coherent
state, which describes classical behavior, but tend to be large otherwise. We
find in all cases studied that the energy density fluctuations are large
whenever the local energy density is negative. This is taken to mean that the
gravitational field of a system with negative energy density, such as the
Casimir vacuum, is not described by a fixed classical metric but is undergoing
large metric fluctuations. We propose an operational scheme by which one can
describe a fluctuating gravitational field in terms of the statistical behavior
of test particles. For this purpose we obtain an equation of the form of the
Langevin equation used to describe Brownian motion.Comment: In REVTEX. 20pp + 4 figures(not included, available upon request)
TUTP-93-
The Effects of Stress Tensor Fluctuations upon Focusing
We treat the gravitational effects of quantum stress tensor fluctuations. An
operational approach is adopted in which these fluctuations produce
fluctuations in the focusing of a bundle of geodesics. This can be calculated
explicitly using the Raychaudhuri equation as a Langevin equation. The physical
manifestation of these fluctuations are angular blurring and luminosity
fluctuations of the images of distant sources. We give explicit results for the
case of a scalar field on a flat background in a thermal state.Comment: 26 pages, 1 figure, new material added in Sect. III and in Appendices
B and
Quantum Inequalities on the Energy Density in Static Robertson-Walker Spacetimes
Quantum inequality restrictions on the stress-energy tensor for negative
energy are developed for three and four-dimensional static spacetimes. We
derive a general inequality in terms of a sum of mode functions which
constrains the magnitude and duration of negative energy seen by an observer at
rest in a static spacetime. This inequality is evaluated explicitly for a
minimally coupled scalar field in three and four-dimensional static
Robertson-Walker universes. In the limit of vanishing curvature, the flat
spacetime inequalities are recovered. More generally, these inequalities
contain the effects of spacetime curvature. In the limit of short sampling
times, they take the flat space form plus subdominant curvature-dependent
corrections.Comment: 18 pages, plain LATEX, with 3 figures, uses eps
Restrictions on Negative Energy Density in Flat Spacetime
In a previous paper, a bound on the negative energy density seen by an
arbitrary inertial observer was derived for the free massless, quantized scalar
field in four-dimensional Minkowski spacetime. This constraint has the form of
an uncertainty principle-type limitation on the magnitude and duration of the
negative energy density. That result was obtained after a somewhat complicated
analysis. The goal of the current paper is to present a much simpler method for
obtaining such constraints. Similar ``quantum inequality'' bounds on negative
energy density are derived for the electromagnetic field, and for the massive
scalar field in both two and four-dimensional Minkowski spacetime.Comment: 17 pages, including two figures, uses epsf, minor revisions in the
Introduction, conclusions unchange
Gravitons and Lightcone Fluctuations II: Correlation Functions
A model of a fluctuating lightcone due to a bath of gravitons is further
investigated. The flight times of photons between a source and a detector may
be either longer or shorter than the light propagation time in the background
classical spacetime, and will form a Gaussian distribution centered around the
classical flight time. However, a pair of photons emitted in rapid succession
will tend to have correlated flight times. We derive and discuss a correlation
function which describes this effect. This enables us to understand more fully
the operational significance of a fluctuating lightcone. Our results may be
combined with observational data on pulsar timing to place some constraints on
the quantum state of cosmological gravitons.Comment: 16 pages and two figures, uses eps
Quantum Field Theory Constrains Traversable Wormhole Geometries
Recently a bound on negative energy densities in four-dimensional Minkowski
spacetime was derived for a minimally coupled, quantized, massless, scalar
field in an arbitrary quantum state. The bound has the form of an uncertainty
principle-type constraint on the magnitude and duration of the negative energy
density seen by a timelike geodesic observer. When spacetime is curved and/or
has boundaries, we argue that the bound should hold in regions small compared
to the minimum local characteristic radius of curvature or the distance to any
boundaries, since spacetime can be considered approximately Minkowski on these
scales. We apply the bound to the stress-energy of static traversable wormhole
spacetimes. Our analysis implies that either the wormhole must be only a little
larger than Planck size or that there is a large discrepancy in the length
scales which characterize the wormhole. In the latter case, the negative energy
must typically be concentrated in a thin band many orders of magnitude smaller
than the throat size. These results would seem to make the existence of
macroscopic traversable wormholes very improbable.Comment: 26 pages, plain LaTe
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
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
Dynamic wormholes
A new framework is proposed for general dynamic wormholes, unifying them with
black holes. Both are generically defined locally by outer trapping horizons,
temporal for wormholes and spatial or null for black and white holes. Thus
wormhole horizons are two-way traversible, while black-hole and white-hole
horizons are only one-way traversible. It follows from the Einstein equation
that the null energy condition is violated everywhere on a generic wormhole
horizon. It is suggested that quantum inequalities constraining negative energy
break down at such horizons. Wormhole dynamics can be developed as for
black-hole dynamics, including a reversed second law and a first law involving
a definition of wormhole surface gravity. Since the causal nature of a horizon
can change, being spatial under positive energy and temporal under sufficient
negative energy, black holes and wormholes are interconvertible. In particular,
if a wormhole's negative-energy source fails, it may collapse into a black
hole. Conversely, irradiating a black-hole horizon with negative energy could
convert it into a wormhole horizon. This also suggests a possible final state
of black-hole evaporation: a stationary wormhole. The new framework allows a
fully dynamical description of the operation of a wormhole for practical
transport, including the back-reaction of the transported matter on the
wormhole. As an example of a matter model, a Klein-Gordon field with negative
gravitational coupling is a source for a static wormhole of Morris & Thorne.Comment: 5 revtex pages, 4 eps figures. Minor change which did not reach
publisher
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