Beltrami-de Sitter时空和de Sitter不变的狭义相对论

分析了在相对论体系中狭义相对性原理和宇宙学原理之间的关系以及Beltrami-de Sitter -陆启铿疑难.指出可以把狭义相对性原理推广到非零常曲率时空，在具有Beltrami度规 的de Sitter/反de Sitter时空中建立狭义相对论的运动学和粒子动力学. 在这类狭义相对 论中,相对于Beltrami坐标同时性，Beltrami坐标系就是惯性坐标系，相应的观测者为惯 性观测者; 对于自由粒子和光讯号, 惯性定律成立;可以定义可观测量,它们不但守恒而且还 满足推广的爱因斯坦关系.除了Beltrami坐标时同时性之外，对于共动观测, 还可以取固 有时同时性;此时，Beltrami度规成为Robertson-Walker型的度规，其3维空间是闭的,对 于平坦的偏离为宇宙学常数的量级.这表明,在这类狭义相对论中,相对性原理与“完美”宇 宙学原理之间存在内在联系,并不存在那些问题.进而,基于最新观测事实，重述了Mach原 理；指出对于Beltrami-de Sitter/反de Sitter时空，宇宙学常数恰恰给出惯性运动的起 源. 关键词： 狭义相对性原理 宇宙学原理 de Sitter不变的狭义相对论 Beltrami-de Sitter时空 同时性 Mach原理     

Lorentz boosts in de Sitter and anti-de Sitter space-times

Symmetries of de Sitter and anti-de Sitter space-times are discussed. In particular, Lorentz boosts, which appear to be given previously only in the infinitesimal form, are presented here in closed finite forms.Dedicated to the memory of Professor Jozef Kvasnica.I would like to thank Prof. Jií Biák and Dr. Hans-Jürgen Schmidt for useful discussions.     

Anomalies and de Sitter radiation from the generic black holes in de Sitter spaces

Robinson–Wilczek's recent work shows that, the energy–momentum tensor flux required to cancel gravitational anomaly at the event horizon of a Schwarzschild-type black hole has an equivalent form to that of a (1+1)$(1+1)$-dimensional blackbody radiation at the Hawking temperature. Motivated by their work, Hawking radiation from the cosmological horizons of the general Schwarzschild–de Sitter and Kerr–de Sitter black holes, has been studied by the method of anomaly cancellation. The result shows that the absorbing gauge current and energy momentum tensor fluxes required to cancel gauge and gravitational anomalies at the cosmological horizon are precisely equal to those of Hawking radiation from it. It should be emphasized that the effective field theory for generic black holes in de Sitter spaces should be formulated within the region between the event horizon (EH) and the cosmological horizon (CH), to integrate out the classically irrelevant ingoing modes at the EH and the classically irrelevant outgoing modes at the CH, respectively.     

Neutrino Oscillations in the de Sitter and the Anti-de Sitter Space-Time

General expressions of the neutrino oscillation phase in the generally static space-time with spherical symmetry are given. The effect of the gravitational field on the oscillation length is embodied in the gravitational red shift factor. We find that a blue shift of the oscillation length takes place when the neutrino travels out of the gravitational field. Then, we discuss the variation of the oscillation length influenced by the cosmological constant. In the de Sitter space-time, the positive cosmological constant prolongs the oscillation length. And, in the anti-de Sitter space-time, the negative cosmological constant shortens it as expected.     

Massive Particles' de Sitter Tunneling in (3+1)-Dimensional de Sitter Spacetimes

In this paper, massive particles' Hawking radiation via tunneling from cosmological horizon of a (3+1)-dimensional de Sitter spacetime is investigated. According to Parikh's theory, when a particle tunnels across the cosmological horizon, the effective geometry is Schwarzschild-de Sitter spacetime. In this effective spacetime, a massive particle can be treated as a de Broglie S-wave. WKB method is used. The emission spectrum is obtained, and it takes the same functional form as that of massless particles.     

Quantum Mechanics in de Sitter Space

We consider some possible phenomenological implications of the extended uncertainty principle, which is believed to hold for quantum mechanics in de Sitter spacetime. The relative size of the corrections to the standard results is however of the order of the ratio between the length scale of the quantum mechanical system and the de Sitter radius, and therefore exceedingly small. Nevertheless, the existence of effects due to the large scale curvature of spacetime in atomic experiments has a theoretical relevance.     

Q-Stars in Anti de Sitter Spacetime

We study q-stars with various symmetries in anti de Sitter spacetime in 3+1 dimensions. Comparing with the case of flat spacetime, we find that the value of the field at the center of the soliton is larger when the other parameters show a more complicated behavior. We also investigate their phase space when the symmetry is local and the effect of the charge to its stability.     

Anisotropic perturbation of de Sitter space

A model-independent expression for the Friedmann equation in Bianchi type spaces is derived. In addition, a model-independent stability analysis of the higher curvature de Sitter solution is discussed. Stability conditions of the de Sitter solution are derived explicitly for a cubic model with interesting effects. It is known that quadratic terms do not contribute to this de Sitter background solution. Higher curvature terms are all critical to the stability of the de Sitter space. PACS 98.80.Cq; 04.20.-q; 04.20.Cv     

The de Sitter universe and mechanics

If we study the de Sitter universe with the methods of projective geometry, we obtain a new mechanics valid on a cosmic scale and for hyperdense matter. In this projective mechanics the mass varies with the space-time distance, and the linear and angular momentum are reunited in a single projective tensor.     

Stochastic behaviour of de Sitter universes

A stochastization procedure applied to mini-universe (friedmons) leads to a nonzero average minimum radius and thus to the exclusion of classical singularities.     

Phase transitions in de Sitter space

An effective potential in de Sitter space is calculated for a model of two interacting scalar fields in one-loop approximation and in a self-consistent approximation which takes into account an infinite set of diagrams. Various approaches to renormalization in de Sitter space are discussed. The results are applied to analyze the phase transition in the Hawking-Moss version of the inflationary universe scenario. Requiring that inflation is sufficiently large, we derive constraints on the parameters of the model.     

Semiclassical perdurance of de Sitter space

We investigate the classical and semiclassical instabilities of de Sitter space. Due to the presence of a cosmological event horizon and its associated Hawking temperature, de Sitter space might be expected to behave in some respects like flat space at finite temperature. We use the euclidean formulation of quantum gravity to show that de Sitter space does exhibit a semiclassical instability to the nucleation of black holes. We find, however, no analog to the classical instability due to gravitational clumping of thermally excited gravitons.