17,873 research outputs found
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 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
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
Cosmological and Black Hole Horizon Fluctuations
The quantum fluctuations of horizons in Robertson-Walker universes and in the
Schwarzschild spacetime are discussed. The source of the metric fluctuations is
taken to be quantum linear perturbations of the gravitational field. Lightcone
fluctuations arise when the retarded Green's function for a massless field is
averaged over these metric fluctuations. This averaging replaces the
delta-function on the classical lightcone with a Gaussian function, the width
of which is a measure of the scale of the lightcone fluctuations. Horizon
fluctuations are taken to be measured in the frame of a geodesic observer
falling through the horizon. In the case of an expanding universe, this is a
comoving observer either entering or leaving the horizon of another observer.
In the black hole case, we take this observer to be one who falls freely from
rest at infinity. We find that cosmological horizon fluctuations are typically
characterized by the Planck length. However, black hole horizon fluctuations in
this model are much smaller than Planck dimensions for black holes whose mass
exceeds the Planck mass. Furthermore, we find black hole horizon fluctuations
which are sufficiently small as not to invalidate the semiclassical derivation
of the Hawking process.Comment: 22 pages, Latex, 4 figures, uses eps
A quantum weak energy inequality for the Dirac field in two-dimensional flat spacetime
Fewster and Mistry have given an explicit, non-optimal quantum weak energy
inequality that constrains the smeared energy density of Dirac fields in
Minkowski spacetime. Here, their argument is adapted to the case of flat,
two-dimensional spacetime. The non-optimal bound thereby obtained has the same
order of magnitude, in the limit of zero mass, as the optimal bound of Vollick.
In contrast with Vollick's bound, the bound presented here holds for all
(non-negative) values of the field mass.Comment: Version published in Classical and Quantum Gravity. 7 pages, 1 figur
Negative Energy Density States for the Dirac Field in Flat Spacetime
Negative energy densities in the Dirac field produced by state vectors that
are the superposition of two single particle electron states are examined. I
show that for such states the energy density of the field is not bounded from
below and that the quantum inequalities derived for scalar fields are
satisfied. I also show that it is not possible to produce negative energy
densities in a scalar field using state vectors that are arbitrary
superpositions of single particle states.Comment: 11 pages, LaTe
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
BATSE Gamma-Ray Burst Line Search: V. Probability of Detecting a Line in a Burst
The physical importance of the apparent discrepancy between the detections by
pre-BATSE missions of absorption lines in gamma-ray burst spectra and the
absence of a BATSE line detection necessitates a statistical analysis of this
discrepancy. This analysis requires a calculation of the probability that a
line, if present, will be detected in a given burst. However, the connection
between the detectability of a line in a spectrum and in a burst requires a
model for the occurrence of a line within a burst. We have developed the
necessary weighting for the line detection probability for each spectrum
spanning the burst. The resulting calculations require a description of each
spectrum in the BATSE database. With these tools we identify the bursts in
which lines are most likely to be detected. Also, by assuming a small frequency
with which lines occur, we calculate the approximate number of BATSE bursts in
which lines of various types could be detected. Lines similar to the Ginga
detections can be detected in relatively few BATSE bursts; for example, in only
~20 bursts are lines similar to the GB 880205 pair of lines detectable. Ginga
reported lines at ~20 and ~40 keV whereas the low energy cutoff of the BATSE
spectra is typically above 20 keV; hence BATSE's sensitivity to lines is less
than that of Ginga below 40 keV, and greater above. Therefore the probability
that the GB 880205 lines would be detected in a Ginga burst rather than a BATSE
burst is ~0.2. Finally, we adopted a more appropriate test of the significance
of a line feature.Comment: 20 pages, AASTeX 4.0, 5 figures, Ap.J. in pres
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
Focusing Vacuum Fluctuations
The focusing of the vacuum modes of a quantized field by a parabolic mirror
is investigated. We use a geometric optics approximation to calculate the
energy density and mean squared field averages for scalar and electromagnetic
fields near the focus. We find that these quantities grow as an inverse power
of the distance to the focus. There is an attractive Casimir-Polder force on an
atom which will draw it into the focus. Some estimates of the magnitude of the
effects of this focusing indicate that it may be observable.Comment: 20 pages, 4 figures; typos corrected, two refs and some comments
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