Space-Time Directional Lyapunov Exponents for Cellular Automata

Space-time directional Lyapunov exponents are introduced. They describe the maximal velocity of propagation to the right or to the left of fronts of perturbations in a frame moving with a given velocity. The continuity of these exponents as function of the velocity and an inequality relating them to the directional entropy is proved.     

Kalman filtering of a space-time Markov random field

In this paper, finite-dimensional recursive filters for space-time Markov random fields are derived. These filters can be used with the expectation maximization (EM) algorithm to yield maximum likelihood estimates of the parameters of the model.     

Cardy-Verlinde Formula and Thermodynamics of Black Hole in Higher Dimensional Space-Time

In this paper we discuss thermodynamics parameters of black hole horizon and cosmological horizon in general high-dimensional space-time. We obtain that the entropy of a cosmological horizon can be described by the Cardy-Verlinde formula. However, the entropy of black hole horizon will be expressed in a form of the Cardy-Verlinde formula, if one adopts the methods given by Abbott and Deser to compute the mass of a black hole in general high-dimensional space-time. Through discussion, relation among various thermodynamics parameters of the black hole in general high-dimensional space-time is given. That is, differential formula of the first law of thermodynamics is obtained. Because we discuss the general high-dimensional space-time, our result has universality. PACS: 04.20.Dw, 97.60.Lf     

Gravitational Collapse of Self-Similar Perfect Fluid in 2 + 1 Gravity

Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. These include all the solutions of dust and stiff perfect fluid with self-similarity of the first kind, and all the solutions of perfect fluid with a linear equation of state and self-similarity of the zeroth and second kinds. It is found that some of these solutions represent gravitational collapse, and the final state of the collapse can be either a black hole or a null singularity. It is also shown that one solution can have two different kinds of kinematic self-similarity.     

Dirac Fields in 3D de Sitter Spacetime

We show that the Dirac equation is separable in the circularly symmetric metric in three dimensions and when the background spacetime is de Sitter we find exact solutions to the radial equations. Using these results we show that the de Sitter horizon has a cross section equal to zero for the massless Dirac field, as in the case of the scalar field. Also, using the improved brick wall model we calculate the fermionic entropy associated with the de Sitter horizon and we compare it with some results previously published.     

Space-Time Topology (II)—Causality, the Fourth Stiefel–Whitney Class and Space-Time as a Boundary

We show that stable causality is related to the vanishing of the top Stiefel–Whitney class of a space-time manifold M, and that if M is a stably causal space-time manifold, then it is the boundary of a five-dimensional space-time. We then propose a scheme for making it both a necessary and sufficient condition.     

De Sitter universes and the emerging landscape in string theory

We discuss a recent proposal to construct de Sitter vacua in string theory. It is based on flux compactifications in string theory where all the moduli are stabilised and supersymmetry is broken with control. The resulting picture is that of a complicated landscape with many vacua of widely varying values for the cosmological constant.     

确定事件视界的新公式

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Research on Hawking Radiation as Tunneling from Schwarzshild-anti-de Sitter Black Hole

After taking into account energy conservation and the particle’s self-gravitation interaction, Hawking radiation of the massive particle as tunneling from Schwarzshild-anti-de Sitter black hole is studied by using Parikh-Wilczek’s semi-classical quantum tunneling approach. Meanwhile, Hawking radiation as tunneling from the black hole is reexamined by developing Angheben–Nadalini–Vanzo–Zerbini (ANVZ) covariant method to cover energy conservation and the particle’s self-gravitation interaction. Both the results perfectly generalize those obtained by Parikh and Wilczek, and show that the tunneling rate is related to the change of Bekenstein-Hawking entropy, and the factual emission spectrum is not exactly thermal, but satisfies the underlying unitary theory. PACS: 04.70-s, 9760. Lf.