19,733 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
Focusing Vacuum Fluctuations II
The quantization of the scalar and electromagnetic fields in the presence of
a parabolic mirror is further developed in the context of a geometric optics
approximation. We extend results in a previous paper to more general
geometries, and also correct an error in one section of that paper. We
calculate the mean squared scalar and electric fields near the focal line of a
parabolic cylindrical mirror. These quantities are found to grow as inverse
powers of the distance from the focus. We give a combination of analytic and
numerical results for the mean squared fields. In particular, we find that the
mean squared electric field can be either negative or positive, depending upon
the choice of parameters. The case of a negative mean squared electric field
corresponds to a repulsive Van der Waals force on an atom near the focus, and
to a region of negative energy density. Similarly, a positive value corresponds
to an attractive force and a possibility of atom trapping in the vicinity of
the focus.Comment: 26 pages, 15 figures; additional discussion added in Sects. IV and I
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
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
Relation Between Einstein And Quantum Field Equations
We show that there exists a choice of scalar field modes, such that the
evolution of the quantum field in the zero-mass and large-mass limits is
consistent with the Einstein equations for the background geometry. This choice
of modes is also consistent with zero production of these particles and thus
corresponds to a preferred vacuum state preserved by the evolution. In the
zero-mass limit, we find that the quantum field equation implies the Einstein
equation for the scale factor of a radiation-dominated universe; in the
large-mass case, it implies the corresponding Einstein equation for a
matter-dominated universe. Conversely, if the classical radiation-dominated or
matter-dominated Einstein equations hold, there is no production of scalar
particles in the zero and large mass limits, respectively. The suppression of
particle production in the large mass limit is over and above the expected
suppression at large mass. Our results hold for a certain class of conformally
ultrastatic background geometries and therefore generalize previous results by
one of us for spatially flat Robertson-Walker background geometries. In these
geometries, we find that the temporal part of the graviton equations reduces to
the temporal equation for a massless minimally coupled scalar field, and
therefore the results for massless particle production hold also for gravitons.
Within the class of modes we study, we also find that the requirement of zero
production of massless scalar particles is not consistent with a non-zero
cosmological constant. Possible implications are discussed.Comment: Latex, 24 pages. Minor changes in text from original versio
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
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
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