1,966 research outputs found
Radiative spacetimes approaching the Vaidya metric
We analyze a class of exact type II solutions of the Robinson-Trautman family
which contain pure radiation and (possibly) a cosmological constant. It is
shown that these spacetimes exist for any sufficiently smooth initial data, and
that they approach the spherically symmetric Vaidya-(anti-)de Sitter metric. We
also investigate extensions of the metric, and we demonstrate that their order
of smoothness is in general only finite. Some applications of the results are
outlined.Comment: 12 pages, 3 figure
Canonical theory of spherically symmetric spacetimes with cross-streaming null dusts
The Hamiltonian dynamics of two-component spherically symmetric null dust is
studied with regard to the quantum theory of gravitational collapse. The
components--the ingoing and outgoing dusts--are assumed to interact only
through gravitation. Different kinds of singularities, naked or "clothed", that
can form during collapse processes are described. The general canonical
formulation of the one-component null-dust dynamics by Bicak and Kuchar is
restricted to the spherically symmetric case and used to construct an action
for the two components. The transformation from a metric variable to the
quasilocal mass is shown to simplify the mathematics. The action is reduced by
a choice of gauge and the corresponding true Hamiltonian is written down.
Asymptotic coordinates and energy densities of dust shells are shown to form a
complete set of Dirac observables. The action of the asymptotic time
translation on the observables is defined but it has been calculated explicitly
only in the case of one-component dust (Vaidya metric).Comment: 15 pages, 3 figures, submitted to Phys. Rev.
Non-Extremality, Chemical Potential and the Infrared limit of Large N Thermal QCD
Non-extremal solution with warped resolved-deformed conifold background is
important to study the infrared limit of large N thermal QCD. Earlier works in
this direction have not taken into account all the back-reactions on the
geometry, namely from the branes, fluxes, and black-hole carefully. In the
present work we make some progress in this direction by solving explicitly the
supergravity equations of motions in the presence of the backreaction from the
black-hole. The backreactions from the branes and the fluxes on the other hand
and to the order that we study, are comparatively suppressed. Our analysis
reveal, among other things, how the resolution parameter would depend on the
horizon radius and how the RG flows of the coupling constants should be
understood in these scenarios, including their effects on the background
three-form fluxes. We also study the effect of switching on a chemical
potential in the background and, in a particularly simplified scenario, compute
the actual value of the chemical potential for our case.Comment: 61 pages, LaTex, 3 eps figures; v2: Some corrections done in sec 2.1
to sharpen the regime of validity of our results. Text expanded, typos
corrected and minor corrections added to the other sections; v3: Text
expanded at various places, typos corrected and references added. Final
version to appear in Physical Review
Schwarzschild Atmospheric Processes: A Classical Path to the Quantum
We develop some classical descriptions for processes in the Schwarzschild
string atmosphere. These processes suggest relationships between macroscopic
and microscopic scales. The classical descriptions developed in this essay
highlight the fundamental quantum nature of the Schwarzschild atmospheric
processes.Comment: to appear in Gen. Rel. Gra
Solving a "Hard" Problem to Approximate an "Easy" One: Heuristics for Maximum Matchings and Maximum Traveling Salesman Problems
We consider geometric instances of the Maximum Weighted Matching Problem
(MWMP) and the Maximum Traveling Salesman Problem (MTSP) with up to 3,000,000
vertices. Making use of a geometric duality relationship between MWMP, MTSP,
and the Fermat-Weber-Problem (FWP), we develop a heuristic approach that yields
in near-linear time solutions as well as upper bounds. Using various
computational tools, we get solutions within considerably less than 1% of the
optimum.
An interesting feature of our approach is that, even though an FWP is hard to
compute in theory and Edmonds' algorithm for maximum weighted matching yields a
polynomial solution for the MWMP, the practical behavior is just the opposite,
and we can solve the FWP with high accuracy in order to find a good heuristic
solution for the MWMP.Comment: 20 pages, 14 figures, Latex, to appear in Journal of Experimental
Algorithms, 200
Balancing Minimum Spanning and Shortest Path Trees
This paper give a simple linear-time algorithm that, given a weighted
digraph, finds a spanning tree that simultaneously approximates a shortest-path
tree and a minimum spanning tree. The algorithm provides a continuous
trade-off: given the two trees and epsilon > 0, the algorithm returns a
spanning tree in which the distance between any vertex and the root of the
shortest-path tree is at most 1+epsilon times the shortest-path distance, and
yet the total weight of the tree is at most 1+2/epsilon times the weight of a
minimum spanning tree. This is the best tradeoff possible. The paper also
describes a fast parallel implementation.Comment: conference version: ACM-SIAM Symposium on Discrete Algorithms (1993
Radiating black hole solutions in arbitrary dimensions
We prove a theorem that characterizes a large family of non-static solutions
to Einstein equations in -dimensional space-time, representing, in general,
spherically symmetric Type II fluid. It is shown that the best known
Vaidya-based (radiating) black hole solutions to Einstein equations, in both
four dimensions (4D) and higher dimensions (HD), are particular cases from this
family. The spherically symmetric static black hole solutions for Type I fluid
can also be retrieved. A brief discussion on the energy conditions,
singularities and horizons is provided.Comment: RevTeX 9 pages, no figure
Holographic Evolution of Entanglement Entropy
We study the evolution of entanglement entropy in a 2-dimensional
equilibration process that has a holographic description in terms of a Vaidya
geometry. It models a unitary evolution in which the field theory starts in a
pure state, its vacuum, and undergoes a perturbation that brings it far from
equilibrium. The entanglement entropy in this set up provides a measurement of
the quantum entanglement in the system. Using holographic techniques we recover
the same result obtained before from the study of processes triggered by a
sudden change in a parameter of the hamiltonian, known as quantum quenches.
Namely, entanglement in 2-dimensional conformal field theories propagates with
velocity v^2=1. Both in quantum quenches and in the Vaidya model equilibration
is only achieved at the local level. Remarkably, the holographic derivation of
this last fact requires information from behind the apparent horizon generated
in the process of gravitational collapse described by the Vaidya geometry. In
the early stages of the evolution the apparent horizon seems however to play no
relevant role with regard to the entanglement entropy. We speculate on the
possibility of deriving a thermalization time for occupation numbers from our
analysis.Comment: 26 pages, 10 figure
On the constitution of sodium at higher densities
Using density functional theory the atomic and electronic structure of sodium
are predicted to depart substantially from those expected of simple metals for
GPa). Newly-predicted phases include those with low
structural symmetry, semi-metallic electronic properties (including zero-gap
semiconducting limiting behavior), unconventional valence charge density
distributions, and even those that raise the possibility of superconductivity,
all at currently achievable pressures. Important differences emerge between
sodium and lithium at high densities, and these are attributable to
corresponding differences in their respective cores.Comment: 13 pages; 3 figure
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