288 research outputs found
The Final State of Black Strings and p-Branes, and the Gregory-Laflamme Instability
It is shown that the usual entropy argument for the Gregory-Laflamme (GL)
instability for appropriate black strings and -branes gives
surprising agreement up to a few percent. This may provide a strong support to
the GL's horizon fragmentation, which would produce the array of
higher-dimensional Schwarzschild-type's black holes finally. On the other hand,
another estimator for the size of the black hole end-state relative to the
compact dimension indicates a second order (i.e., smooth) phase transition for
some appropriate compactifications and total dimension of spacetime
wherein the entropy argument is not appropriate. In this case,
Horowitz-Maeda-type's non-uniform black strings or -branes can be the final
state of the GL instability.Comment: More emphasis on a second order phase transition. The computation
result is unchange
Three-slit experiments and quantum nonlocality
An interesting link between two very different physical aspects of quantum
mechanics is revealed; these are the absence of third-order interference and
Tsirelson's bound for the nonlocal correlations. Considering multiple-slit
experiments - not only the traditional configuration with two slits, but also
configurations with three and more slits - Sorkin detected that third-order
(and higher-order) interference is not possible in quantum mechanics. The EPR
experiments show that quantum mechanics involves nonlocal correlations which
are demonstrated in a violation of the Bell or CHSH inequality, but are still
limited by a bound discovered by Tsirelson. It now turns out that Tsirelson's
bound holds in a broad class of probabilistic theories provided that they rule
out third-order interference. A major characteristic of this class is the
existence of a reasonable calculus of conditional probability or, phrased more
physically, of a reasonable model for the quantum measurement process.Comment: 9 pages, no figur
Stable Topologies of Event Horizon
In our previous work, it was shown that the topology of an event horizon (EH)
is determined by the past endpoints of the EH. A torus EH (the collision of two
EH) is caused by the two-dimensional (one-dimensional) set of the endpoints. In
the present article, we examine the stability of the topology of the EH. We see
that a simple case of a single spherical EH is unstable. Furthermore, in
general, an EH with handles (a torus, a double torus, ...) is structurally
stable in the sense of catastrophe theory.Comment: 21 pages, revtex, five figures containe
One-Dimensional Approximation of Viscous Flows
Attention has been paid to the similarity and duality between the
Gregory-Laflamme instability of black strings and the Rayleigh-Plateau
instability of extended fluids. In this paper, we derive a set of simple
(1+1)-dimensional equations from the Navier-Stokes equations describing thin
flows of (non-relativistic and incompressible) viscous fluids. This
formulation, a generalization of the theory of drop formation by Eggers and his
collaborators, would make it possible to examine the final fate of
Rayleigh-Plateau instability, its dimensional dependence, and possible
self-similar behaviors before and after the drop formation, in the context of
fluid/gravity correspondence.Comment: 17 pages, 3 figures; v2: refs & comments adde
Effective theory for close limit of two branes
We discuss the effective theory for the close limit of two branes in a
covariant way. To do so we solve the five dimensional Einstein equation along
the direction of the extra dimension. Using the Taylor expansion we solve the
bulk spacetimes and derive the effective theory describing the close limit. We
also discuss the radion dynamics and braneworld black holes for the close limit
in our formulation.Comment: 6 pages, a version to be published in Phy.Rev.
Double-slit interference pattern from single-slit screen and its gravitational analogues
The double slit experiment (DSE) is known as an important cornerstone in the
foundations of physical theories such as Quantum Mechanics and Special
Relativity. A large number of different variants of it were designed and
performed over the years. We perform and discuss here a new verion with the
somewhat unexpected results of obtaining interference pattern from single-slit
screen. This outcome, which shows that the routes of the photons through the
array were changed, leads one to discuss it, using the equivalence principle,
in terms of geodesics mechanics. We show using either the Brill's version of
the canonical formulation of general relativity or the linearized version of it
that one may find corresponding and analogous situations in the framework of
general relativity.Comment: 51 pages, 12 Figures five of them contain two subfigures and thus the
number of figures is 17, 1 Table. Some minor changes introduced, especially,
in the reference
Lorentzian and Euclidean Quantum Gravity - Analytical and Numerical Results
We review some recent attempts to extract information about the nature of
quantum gravity, with and without matter, by quantum field theoretical methods.
More specifically, we work within a covariant lattice approach where the
individual space-time geometries are constructed from fundamental simplicial
building blocks, and the path integral over geometries is approximated by
summing over a class of piece-wise linear geometries. This method of
``dynamical triangulations'' is very powerful in 2d, where the regularized
theory can be solved explicitly, and gives us more insights into the quantum
nature of 2d space-time than continuum methods are presently able to provide.
It also allows us to establish an explicit relation between the Lorentzian- and
Euclidean-signature quantum theories. Analogous regularized gravitational
models can be set up in higher dimensions. Some analytic tools exist to study
their state sums, but, unlike in 2d, no complete analytic solutions have yet
been constructed. However, a great advantage of our approach is the fact that
it is well-suited for numerical simulations. In the second part of this review
we describe the relevant Monte Carlo techniques, as well as some of the
physical results that have been obtained from the simulations of Euclidean
gravity. We also explain why the Lorentzian version of dynamical triangulations
is a promising candidate for a non-perturbative theory of quantum gravity.Comment: 69 pages, 16 figures, references adde
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
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