Choice Of Slice Research Articles

Quantum evolution of the Hawking state for black holes

We give a general description of the evolving quantum state of a Schwarzschild black hole, in the quantum field theory approximation. Such a time-dependent description is based on introducing a choice of time slices. We in particular consider slices that smoothly cross the horizon, and introduction of "stationary" such slices simplifies the analysis. This analysis goes beyond standard derivations of Hawking radiation that focus on asymptotic excitations, and in particular gives an evolving state that is regular at the horizon, with no explicit transplanckian dependence, and that can in principle be generalized to incorporate interacting fields. It is also expected to be useful in connecting to information-theoretic investigation of black hole evolution. The description of the evolving state depends on the choice of slices as well as coordinates on the slices and mode bases; these choices give different "pictures" analogous to that of Schr\"odinger. Evolution does have a simpler appearance in an energy eigenbasis, but such a basis is also singular at the horizon; evolution of regular modes has a more complicated appearance, whose properties may be inferred by comparing with the energy eigenbasis. In a regular description, Hawking quanta are produced in a black hole atmosphere, at scales comparable to the horizon size. This approach is also argued to extend to more general asymptotics, such as that of anti de Sitter space. In the latter context, this analysis provides a description of the hamiltonian and evolution of a black hole that may be compared to the large-$N$ dynamics of the proposed dual CFT.

On information fusion to improve segmentation of MRI sequences

Abstract The paper deals with the problem of segmentation of MRI sequences of vertebrae, in the form of images of their multiple slices, using the Dempster–Shafer theory. This leads to the study of 3-D deformations of the scoliosis. The motivation comes from the inadequacy of the existing techniques based on X-ray image analysis. Such analysis cannot deal with, on the one hand, the complex anatomical structures (“scoliotic rachis”), and the spongy tissue peri-rachidian, and, on the other hand, the choice of slices and the problem of the residue irradiation present in each examination. The main contributions of the paper are: • New architecture for the fusion of MRI data sets. • A novel method to exploit the information contained in MRI sequence. • Model for knowledge representation adapted to specificity of information available (Dempster–Shafer theory). • Choice of the discriminating parameters for the statistical expertise. • Construction of the belief functions. • Choice of the decision criterion. Starting from segmentation by active contour (snake) [Deformable contour: modelling, extraction, detection and classification, Ph.D. Thesis, Wisconsin–Madison University, 1994; Proceedings of the 15th International Conference on Pattern Recognition, vol. 4, Barcelona, 2000, p. 17; Int. J. Comput. Vision 1 (3) (1987) 211], we upgrade it in an attempt to present the doctor with a degree of belief concerning their membership of the contour of the vertebra. We illustrate the proposed fusion architecture by application to actual MRI sequences of the vertebrae, and include perhaps the first example of 3-D reconstruction of the lumbar rachis starting from the results obtained during fusion.

Signal reconstruction from accumulation of bispectral radial slices

The problem of reconstructing signals from their noisy and randomly shifted observations is considered. Our approach is different from existing methods in the choice of slices in the bispectrum domain. Up to now only a single 45 deg slice or multiple parallel-to-axis slices have been used to recover signals. These algorithms either are prone to low signal-to-noise ratio (SNR) estimates or improve SNR of high frequency estimates only. We propose an algorithm that accumulates multiple bispectral radial slices and use the accumulation to recover both the Fourier phase and the magnitude of the signal. Major advantages of the new algorithm are the reduced estimation errors and improvement in SNR in the whole frequency band. A mathematical formulation of the algorithm is given and fast algorithms are presented along with other implementation issues. Performance is evaluated using both simulated data and real radar data. Experimental results show that the proposed algorithm compares favorably with existing methods in terms of mean squared reconstruction error and computational complexity.

Conformal hyperbolic formulation of the Einstein equations

We propose a reformulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the nonconformal degrees of freedom with the latter satisfying a first order strongly hyperbolic system. The conformal degrees of freedom are taken to be determined by the choice of slicing and the initial data, and are regarded as given functions (along with the lapse and the shift) in the hyperbolic part of the evolution. We find that there is a two parameter family of hyperbolic systems for the nonconformal degrees of freedom for a given set of trace free variables. The two parameters are uniquely fixed if we require the system to be ``consistently trace-free,'' i.e., the time derivatives of the trace free variables remain trace-free to the principal part, even in the presence of constraint violations due to numerical truncation error. We show that by forming linear combinations of the trace free variables a conformal hyperbolic system with only physical characteristic speeds can also be constructed.

Trapped surfaces in the Schwarzschild geometry and cosmic censorship.

We prove that in extended Schwarzschild spacetime there exists a family of Cauchy surfaces which come arbitrarily close to the black-hole singularity at r=0 but are such that there do not exist any outer trapped surfaces lying within the past of any of these Cauchy surfaces. We argue that, in any spherically symmetric spacetime describing gravitational collapse to a Schwarzschild black hole, it should be possible to choose a spacelike slicing by Cauchy surfaces which terminates when a singularity (outside the matter) is reached, such that the region of the spacetime covered by the slicing contains no outer trapped surfaces. Thus, an important feature of the numerical collapse examples of Shapiro and Teukolsky, cited by them as evidence against cosmic censorship, does not appear to be qualitatively different from features which occur (for an appropriate choice of slicing) in the standard examples of collapse to a black hole.