13 research outputs found
A Distinguished Vacuum State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology
We define a distinguished "ground state" or "vacuum" for a free scalar
quantum field in a globally hyperbolic region of an arbitrarily curved
spacetime. Our prescription is motivated by the recent construction of a
quantum field theory on a background causal set using only knowledge of the
retarded Green's function. We generalize that construction to continuum
spacetimes and find that it yields a distinguished vacuum or ground state for a
non-interacting, massive or massless scalar field. This state is defined for
all compact regions and for many noncompact ones. In a static spacetime we find
that our vacuum coincides with the usual ground state. We determine it also for
a radiation-filled, spatially homogeneous and isotropic cosmos, and show that
the super-horizon correlations are approximately the same as those of a thermal
state. Finally, we illustrate the inherent non-locality of our prescription
with the example of a spacetime which sandwiches a region with curvature
in-between flat initial and final regions
Enhanced Geometry Fluctuations in Minkowski and Black Hole Spacetimes
We will discuss selected physical effects of spacetime geometry fluctuations,
especially the operational signatures of geometry fluctuations and their
effects on black hole horizons. The operational signatures which we discuss
involve the effects of the fluctuations on images, and include luminosity
variations, spectral line broadening and angular blurring. Our main interest
will be in black hole horizon fluctuations, especially horizon fluctuations
which have been enhanced above the vacuum level by gravitons or matter in
squeezed states. We investigate whether these fluctuations can alter the
thermal character of a black hole. We find that this thermal character is
remarkably robust, and that Hawking's original derivation using transplanckian
modes does not seem to be sensitive even to enhanced horizon fluctuations.Comment: 13 pages, 3 figures, based on a talk presented at the Peyresq 12
worksho
Quantum Fields in Nonstatic background: A Histories Perspective
For a quantum field living on a non - static spacetime no instantaneous
Hamiltonian is definable, for this generically necessitates a choice of
inequivalent representation of the canonical commutation relations at each
instant of time. This fact suggests a description in terms of time - dependent
Hilbert spaces, a concept that fits naturally in a (consistent) histories
framework. Our primary tool for the construction of the quantum theory in a
continuous -time histories format is the recently developed formalism based on
the notion of the history group . This we employ to study a model system
involving a 1+1 scalar field in a cavity with moving boundaries.
The instantaneous (smeared) Hamiltonian and a decoherence functional are then
rigorously defined so that finite values for the time - averaged particle
creation rate are obtainable through the study of energy histories. We also
construct the Schwinger - Keldysh closed- time - path generating functional as
a ``Fourier transform'' of the decoherence functional and evaluate the
corresponding n - point functions.Comment: 27 pages, LATEX; minor changes and corrections; version to appear in
JM
Stochastic Gravity: A Primer with Applications
Stochastic semiclassical gravity of the 90's is a theory naturally evolved
from semiclassical gravity of the 70's and 80's. It improves on the
semiclassical Einstein equation with source given by the expectation value of
the stress-energy tensor of quantum matter fields in curved spacetimes by
incorporating an additional source due to their fluctuations. In stochastic
semiclassical gravity the main object of interest is the noise kernel, the
vacuum expectation value of the (operator-valued) stress-energy bi-tensor, and
the centerpiece is the (stochastic) Einstein-Langevin equation. We describe
this new theory via two approaches: the axiomatic and the functional. The
axiomatic approach is useful to see the structure of the theory from the
framework of semiclassical gravity. The functional approach uses the
Feynman-Vernon influence functional and the Schwinger-Keldysh close-time-path
effective action methods which are convenient for computations. It also brings
out the open systems concepts and the statistical and stochastic contents of
the theory such as dissipation, fluctuations, noise and decoherence. We then
describe the application of stochastic gravity to the backreaction problems in
cosmology and black hole physics. Intended as a first introduction to this
subject, this article places more emphasis on pedagogy than completeness.Comment: 46 pages Latex. Intended as a review in {\it Classical and Quantum
Gravity
Stochastic Gravity: Theory and Applications
Whereas semiclassical gravity is based on the semiclassical Einstein equation
with sources given by the expectation value of the stress-energy tensor of
quantum fields, stochastic semiclassical gravity is based on the
Einstein-Langevin equation, which has in addition sources due to the noise
kernel.In the first part, we describe the fundamentals of this new theory via
two approaches: the axiomatic and the functional. In the second part, we
describe three applications of stochastic gravity theory. First, we consider
metric perturbations in a Minkowski spacetime: we compute the two-point
correlation functions for the linearized Einstein tensor and for the metric
perturbations. Second, we discuss structure formation from the stochastic
gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in
the gravitational background of a quasi-static black hole.Comment: 75 pages, no figures, submitted to Living Reviews in Relativit
Stochastic Gravity: Theory and Applications
Whereas semiclassical gravity is based on the semiclassical Einstein equation
with sources given by the expectation value of the stress-energy tensor of
quantum fields, stochastic semiclassical gravity is based on the
Einstein-Langevin equation, which has in addition sources due to the noise
kernel. In the first part, we describe the fundamentals of this new theory via
two approaches: the axiomatic and the functional. In the second part, we
describe three applications of stochastic gravity theory. First, we consider
metric perturbations in a Minkowski spacetime, compute the two-point
correlation functions of these perturbations and prove that Minkowski spacetime
is a stable solution of semiclassical gravity. Second, we discuss structure
formation from the stochastic gravity viewpoint. Third, we discuss the
backreaction of Hawking radiation in the gravitational background of a black
hole and describe the metric fluctuations near the event horizon of an
evaporating black holeComment: 100 pages, no figures; an update of the 2003 review in Living Reviews
in Relativity gr-qc/0307032 ; it includes new sections on the Validity of
Semiclassical Gravity, the Stability of Minkowski Spacetime, and the Metric
Fluctuations of an Evaporating Black Hol
Dark Energy and Gravity
I review the problem of dark energy focusing on the cosmological constant as
the candidate and discuss its implications for the nature of gravity. Part 1
briefly overviews the currently popular `concordance cosmology' and summarises
the evidence for dark energy. It also provides the observational and
theoretical arguments in favour of the cosmological constant as the candidate
and emphasises why no other approach really solves the conceptual problems
usually attributed to the cosmological constant. Part 2 describes some of the
approaches to understand the nature of the cosmological constant and attempts
to extract the key ingredients which must be present in any viable solution. I
argue that (i)the cosmological constant problem cannot be satisfactorily solved
until gravitational action is made invariant under the shift of the matter
lagrangian by a constant and (ii) this cannot happen if the metric is the
dynamical variable. Hence the cosmological constant problem essentially has to
do with our (mis)understanding of the nature of gravity. Part 3 discusses an
alternative perspective on gravity in which the action is explicitly invariant
under the above transformation. Extremizing this action leads to an equation
determining the background geometry which gives Einstein's theory at the lowest
order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy,
edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure