6,022 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
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
Structural Changes of Yellow Cameleon Domains Observed by Quantitative FRET Analysis and Polarized Fluorescence Correlation Spectroscopy
Förster resonance energy transfer (FRET) is a widely used method for monitoring interactions between or within biological macromolecules conjugated with suitable donor-acceptor pairs. Donor fluorescence lifetimes in absence and presence of acceptor molecules are often measured for the observation of FRET. However, these lifetimes may originate from interacting and noninteracting molecules, which hampers quantitative interpretation of FRET data. We describe a methodology for the detection of FRET that monitors the rise time of acceptor fluorescence on donor excitation thereby detecting only those molecules undergoing FRET. The large advantage of this method, as compared to donor fluorescence quenching method used more commonly, is that the transfer rate of FRET can be determined accurately even in cases where the FRET efficiencies approach 100% yielding highly quenched donor fluorescence. Subsequently, the relative orientation between donor and acceptor chromophores is obtained from time-dependent fluorescence anisotropy measurements carried out under identical conditions of donor excitation and acceptor detection. The FRET based calcium sensor Yellow Cameleon 3.60 (YC3.60) was used because it changes its conformation on calcium binding, thereby increasing the FRET efficiency. After mapping distances and orientation angles between the FRET moieties in YC3.60, cartoon models of this FRET sensor with and without calcium could be created. Independent support for these representations came from experiments where the hydrodynamic properties of YC3.60 under ensemble and single-molecule conditions on selective excitation of the acceptor were determined. From rotational diffusion times as found by fluorescence correlation spectroscopy and consistently by fluorescence anisotropy decay analysis it could be concluded that the open structure (without calcium) is flexible as opposed to the rather rigid closed conformation. The combination of two independent methods gives consistent results and presents a rapid and specific methodology to analyze structural and dynamical changes in a protein on ligand bindin
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
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.
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
van Vleck determinants: traversable wormhole spacetimes
Calculating the van Vleck determinant in traversable wormhole spacetimes is
an important ingredient in understanding the physical basis behind Hawking's
chronology protection conjecture. This paper presents extensive computations of
this object --- at least in the short--throat flat--space approximation. An
important technical trick is to use an extension of the usual junction
condition formalism to probe the full Riemann tensor associated with a thin
shell of matter. Implications with regard to Hawking's chronology protection
conjecture are discussed. Indeed, any attempt to transform a single isolated
wormhole into a time machine results in large vacuum polarization effects
sufficient to disrupt the internal structure of the wormhole before the onset
of Planck scale physics, and before the onset of time travel. On the other
hand, it is possible to set up a putative time machine built out of two or more
wormholes, each of which taken in isolation is not itself a time machine. Such
``Roman configurations'' are much more subtle to analyse. For some particularly
bizarre configurations (not traversable by humans) the vacuum polarization
effects can be arranged to be arbitrarily small at the onset of Planck scale
physics. This indicates that the disruption scale has been pushed down into the
Planck slop. Ultimately, for these configurations, questions regarding the
truth or falsity of Hawking's chronology protection can only be addressed by
entering the uncharted wastelands of full fledged quantum gravity.Comment: 42 pages, ReV_TeX 3.
From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture
The recent interest in ``time machines'' has been largely fueled by the
apparent ease with which such systems may be formed in general relativity,
given relatively benign initial conditions such as the existence of traversable
wormholes or of infinite cosmic strings. This rather disturbing state of
affairs has led Hawking to formulate his Chronology Protection Conjecture,
whereby the formation of ``time machines'' is forbidden. This paper will use
several simple examples to argue that the universe appears to exhibit a
``defense in depth'' strategy in this regard. For appropriate parameter regimes
Casimir effects, wormhole disruption effects, and gravitational back reaction
effects all contribute to the fight against time travel. Particular attention
is paid to the role of the quantum gravity cutoff. For the class of model
problems considered it is shown that the gravitational back reaction becomes
large before the Planck scale quantum gravity cutoff is reached, thus
supporting Hawking's conjecture.Comment: 43 pages,ReV_TeX,major revision
Energy conditions in f(R) gravity and Brans-Dicke theories
The equivalence between f(R) gravity and scalar-tensor theories is invoked to
study the null, strong, weak and dominant energy conditions in Brans-Dicke
theory. We consider the validity of the energy conditions in Brans-Dicke theory
by invoking the energy conditions derived from a generic f(R) theory. The
parameters involved are shown to be consistent with an accelerated expanding
universe.Comment: 9 pages, 1 figure, to appear in IJMP
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