253,631 research outputs found
Black hole evaporation: A paradigm
A paradigm describing black hole evaporation in non-perturbative quantum
gravity is developed by combining two sets of detailed results: i) resolution
of the Schwarzschild singularity using quantum geometry methods; and ii)
time-evolution of black holes in the trapping and dynamical horizon frameworks.
Quantum geometry effects introduce a major modification in the traditional
space-time diagram of black hole evaporation, providing a possible mechanism
for recovery of information that is classically lost in the process of black
hole formation. The paradigm is developed directly in the Lorentzian regime and
necessary conditions for its viability are discussed. If these conditions are
met, much of the tension between expectations based on space-time geometry and
structure of quantum theory would be resolved.Comment: 21 pages, 4 figures, v2: new references and discussion of relation to
other idea
Information is Not Lost in the Evaporation of 2-dimensional Black Holes
We analyze Hawking evaporation of the Callen-Giddings-Harvey-Strominger
(CGHS) black holes from a quantum geometry perspective and show that
information is not lost, primarily because the quantum space-time is
sufficiently larger than the classical. Using suitable approximations to
extract physics from quantum space-times we establish that: i)future null
infinity of the quantum space-time is sufficiently long for the the past vacuum
to evolve to a pure state in the future; ii) this state has a finite norm in
the future Fock space; and iii) all the information comes out at future
infinity; there are no remnants.Comment: 4 pages, 2 figure
Sums over geometries and improvements on the mean field approximation
The saddle points of a Lagrangian due to Efetov are analyzed. This Lagrangian
was originally proposed as a tool for calculating systematic corrections to the
Bethe approximation, a mean-field approximation which is important in
statistical mechanics, glasses, coding theory, and combinatorial optimization.
Detailed analysis shows that the trivial saddle point generates a sum over
geometries reminiscent of dynamically triangulated quantum gravity, which
suggests new possibilities to design sums over geometries for the specific
purpose of obtaining improved mean field approximations to -dimensional
theories. In the case of the Efetov theory, the dominant geometries are locally
tree-like, and the sum over geometries diverges in a way that is similar to
quantum gravity's divergence when all topologies are included. Expertise from
the field of dynamically triangulated quantum gravity about sums over
geometries may be able to remedy these defects and fulfill the Efetov theory's
original promise. The other saddle points of the Efetov Lagrangian are also
analyzed; the Hessian at these points is nonnormal and pseudo-Hermitian, which
is unusual for bosonic theories. The standard formula for Gaussian integrals is
generalized to nonnormal kernels.Comment: Accepted for publication in Physical Review D, probably in November
2007. At the reviewer's request, material was added which made the article
more assertive, confident, and clear. No changes in substanc
A Geometric Variational Approach to Bayesian Inference
We propose a novel Riemannian geometric framework for variational inference
in Bayesian models based on the nonparametric Fisher-Rao metric on the manifold
of probability density functions. Under the square-root density representation,
the manifold can be identified with the positive orthant of the unit
hypersphere in L2, and the Fisher-Rao metric reduces to the standard L2 metric.
Exploiting such a Riemannian structure, we formulate the task of approximating
the posterior distribution as a variational problem on the hypersphere based on
the alpha-divergence. This provides a tighter lower bound on the marginal
distribution when compared to, and a corresponding upper bound unavailable
with, approaches based on the Kullback-Leibler divergence. We propose a novel
gradient-based algorithm for the variational problem based on Frechet
derivative operators motivated by the geometry of the Hilbert sphere, and
examine its properties. Through simulations and real-data applications, we
demonstrate the utility of the proposed geometric framework and algorithm on
several Bayesian models
An Uneventful Horizon in Two Dimensions
We investigate the possibility of firewalls in the Einstein-dilaton gravity
model of CGHS. We use the results of the numerical simulation carried out by
Ashtekar et al. to demonstrate that firewalls are absent and the horizon is
drama free. We show that the lack of a firewall is consistent because the model
does not satisfy one of the postulates of black hole complementarity. In
particular, we show that the Hawking radiation is not pure, and is completely
entangled with a long-lived remnant beyond the last ray.Comment: 28 pages, 4 figure
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