3,256 research outputs found
Generalized retarded integral inequalities
We prove some new retarded integral inequalities. The results generalize
those in [J. Math. Anal. Appl. 301 (2005), no. 2, 265--275].Comment: Changes suggested by the referee don
On some generalizations of certain retarded nonlinear integral inequalities with iterated integrals and an application in retarded differential equation
AbstractIn this paper, we investigate some new nonlinear retarded integral inequalities of Gronwall–Bellman–Pachpatte type. These inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlinear retarded differential and integral equations. An application is also presented to illustrate the usefulness of some of our results in estimation of solution of certain retarded nonlinear differential equations with the initial conditions
Another Look at Bell's Inequalities and Quantum Mechanics
Feynman's path integrals provide a hidden variable description of quantum
mechanics (and quantum field theories). The expectation values defined through
path integrals obey Bell's inequalities in Euclidean time, but not in Minkowski
time. This observation allows us to pinpoint the origin of violation of Bell's
inequalities in quantum mechanics. % This article is not precise enough for
mathematicians and not vague % enough for philosophers, but it should be
interesting for physicists. % Contributed to the XVI International Symposium on
Lepton-Photon % Interactions, Cornell University, August 10-15, 1993.Comment: uses harvmac, 10 pages, IISc-CTS-5/9
Non-equilibrium dynamics and Robinson-Trautman
The Robinson-Trautman space-times provide solutions of Einstein's equations
with negative cosmological constant, which settle to Schwarzschild
black hole at late times. Via gauge/gravity duality they should describe a
system out of equilibrium that evolves towards thermalization. We show that the
area of the past apparent horizon of these space-times satisfies a generalized
Penrose inequality and we formulate as well as provide evidence for a suitable
generalization of Thorne's hoop conjecture. We also compute the holographic
energy-momentum tensor and deduce its late time behavior. It turns out that the
complete non-equilibrium process on the boundary is governed by Calabi's flow
on . Upon linearization, only special modes that arise as supersymmetric
zero energy states of an associated supersymmetric quantum mechanics problem
contribute to the solution. We find that each pole of radiation has an
effective viscosity given by the eigenvalues of the Laplace operator on
and there is an apparent violation of the KSS bound on for the low
lying harmonics of large black holes. These modes, however, do not
satisfy Dirichlet boundary conditions, they are out-going and they do not
appear to have a Kruskal extension across the future horizon .Comment: 48 pages, 2 figures, v2: new section on entropy current, refs added,
JHEP versio
On Quantum Spacetime and the horizon problem
In the special case of a spherically symmetric solution of Einstein equations
coupled to a scalar massless field, we examine the consequences on the exact
solution imposed by a semiclassical treatment of gravitational interaction when
the scalar field is quantized. In agreement with the work of Doplicher,
Fredenhagen and Roberts (DFR), imposing the principle of gravitational
stability against localization of events, we find that the region where an
event is localized, or where initial conditions can be assigned, has a minimal
extension, of the order of the Planck length. This conclusion, though limited
to the case of spherical symmetry, is more general than that of DFR, since it
does not require the use of the notion of energy through the Heisenberg
Principle, nor of any approximation as the linearized Einstein equations.
We shall then describe the influence of this minimal length scale in a
cosmological model, namely a simple universe filled with radiation, which is
effectively described by a conformally coupled scalar field in a conformal KMS
state. Solving the backreaction, a power law inflation scenario appears close
to the initial singularity. Furthermore, the initial singularity becomes light
like and thus the standard horizon problem is avoided in this simple model.
This indication goes in the same direction as those drawn at a heuristic level
from a full use of the principle of gravitational stability against
localization of events, which point to a background dependence of the effective
Planck length, through which a-causal effects may be transmitted.Comment: 26 pages. v3: several discussions and clarifications added, misprints
correcte
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