Determination of all Petrov type-N space-times on which the conformally invariant scalar wave equation satisfies Huygen's principle

It is shown that the conformally invariant wave equation on a Petrov type-N space-time satisfies Huygens' principle if and only if the space-time is conformally related to a plane wave space-time.     

Thermodynamics of de Sitter Black Holes in Massive Gravity

In this paper, by taking de Sitter space-time as a thermodynamic system, we study the effective thermodynamic quantities of de Sitter black holes in massive gravity, and furthermore obtain the effective thermodynamic quantities of the space-time. Our results show that the entropy of this type of space-time takes the same form as that in Reissner-Nordstr¨om-de Sitter space-time, which lays a solid foundation for deeply understanding the universal thermodynamic characteristics of de Sitter space-time in the future. Moreover, our analysis indicates that the effective thermodynamic quantities and relevant parameters play a very important role in the investigation of the stability and evolution of de Sitter space-time.     

Construction and properties of space-timeb-boundaries

A criterion is given for two curves of finite generalized affine length to define the same point of the b-boundary of a space-time. It is shown that the b-boundary can be constructed on every closed subbundle of the bundle of linear frames to which the Levi-Civita connection is reducible. It follows that, for any product space-time, the space-time together with its b-boundary is homeomorphic to a product of pseudo-Riemannian spaces with b-boundary. Furthermore, it is shown that maps of one space-time in to another which are isomorphisms of the connections can be C⁰-extended to the space-time with b-boundary. In particular, it follows that the group of affine transformations and the group of isometries of a space-time act as topological transformation groups on the spacetime with b-boundary.     

Principle of event symmetry

To accommodate topology change, the symmetry of space-time must be extended from the diffeomorphism group of a manifold to the symmetric group acting on the discrete set of space-time events. This is the principle ofevent-symmetric space-time. I investigate a number of physical toy models with this symmetry to gain some insight into the likely nature of event-symmetric space-time. In the more advanced models the symmetric group is embedded into larger structures such as matrix groups which provide scope to unify space-time symmetry with the internal gauge symmetries of particle physics. I also suggest that the symmetric group of space-time could be related to the symmetric group acting to exchange identical particles, implying a unification of space-time and matter. I end with a definition of a new type of loop symmetry which is important in event-symmetric superstring theory.     

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.     

Torsion-induced spin precession

We investigate the motion of a spinning test particle in a spatially-flat FRW-type space-time in the framework of the Einstein–Cartan theory. The space-time has a torsion arising from a spinning fluid filling the space-time. We show that, for spinning particles with non-zero transverse spin components, the torsion induces a precession of the particle spin around the direction of the spin of the fluid. We also show that a charged spinning particle moving in a torsion-less spatially-flat FRW space-time in the presence of a uniform magnetic field undergoes a precession of a different character.     

The topology of geodesically complete space-times

Two theorems are given on the topology of geodesically complete space-times which satisfy the energy condition. Firstly, the condition that a compact embedded 3-manifold in space-time be dentless is defined in terms of causal structure. Then it is shown that a dentless 3-manifold must separate space-time, and that it must enclose a compact portion of space-time. Further, it is shown that if the dentless 3-manifold is homeomorphic toS ³ then the part of space-time that it encloses must be simply connected.     

运动平台混响的时空耦合统计模型

混响时空耦合特性是空时处理混响抑制方法中的关键问题之一。传统方法不是建立在统计模型基础上的,对实际海洋混响扩展、海洋混响环境影响及基阵非理想性导致的混响时空耦合分析缺乏有效性。论文在混响概率模型基础上,推导了运动平台的混响时空耦合关系,进一步给出了复杂水声混响环境及具体阵列指向特性下的混响时空耦合规律的统计模型。利用该模型,推导了理想窄波束基阵混响的时空耦合关系。理论解析结果和计算机仿真清晰地展示了理想阵列流形的混响时空分布规律,验证了本文理论推导结果的正确性。最后采用数值计算方法分析非理想基阵的混响空时耦合关系及空时分布规律,结果表明利用本文的混响空时耦合模型,能获得实际基阵的混响空时分布规律,可为空时处理混响抑制算法与系统设计提供一定的理论支撑。      

Homothetic motions with null homothetic bivectors in general relativity

It is shown that if a nonflat vacuum space-time admits a homothetic vector field with a null homothetic bivector then that space-time is algebraically special. If that homothetic vector field is a nontrivial one (not a Killing one) then the space-time is Petrov type III orN.     

Classical Spontaneous Breakdown of Symmetry and Induction of Inertia

We consider the existing forms of inertia-free mechanics as attempts to reduce the a priori properties of space-time and to search for the mechanism inducing the actual properties of local space-time regions by the matter-distribution in the universe. We explicate the problem of the induction of the local Lorentz structure of space-time and establish a first solution.     

Completeness of the Alexandrov topology for space-time

We show that the Alexandrov topology for a subsetX of a space-time with nondegenerate space-time metric is complete iffX is strongly causal. Therefore, the property of the Alexandrov topology being complete and the property of being Hausdorff coincide. There is thus no physically measurable distinction between the Hausdorff nature and the completeness of the Alexandrov topology for space-time.     

Magnetohydrodynamics in a Riemann-Cartan space-time

By assuming that Maxwell's electromagnetic field equations are valid in a Riemann-Cartan space-time and by using a set of rules to transform from Riemannian kinematics to Riemann-Cartan kinematics, the kinematic aspects of magnetohydrodynamics in a Riemann-Cartan space-time are examined. If the electric conductivity of the fluid is infinite, then the magnetic field conservation laws still hold, but torsion affects the physical interpretation of the equation for proper charge density. A result, based on the Ricci identity foru _a and the first Bianchi identity, and describing differential rotation of a charged fluid in a Riemann space-time, is extended to a Riemann-Cartan space-time. The kinematic role played by torsion in this result is examined.     

T4 gauge theory of gravity and new general relativity

We formulate a space-time translationT ₄ gauge theory of gravity on the Minkowski space-time with appropriate choice of the Lagrangian. By comparing the energy-momentum law of this theory with that of new general relativity constructed on the Weitzenböck space-time we find that in the classical limit the gauge potentials correspond to the parallel vector fields in the Weitzenböck space-time and the gauge field equation coincides with the field equation of gravity in new general relativity in the linearized version. Thus we conclude that in the classical limit theT ₄ gauge theory of gravity leads to the new general relativity.     

The generalized radiation gauge in curved space-time

In the following we give a necessary and sufficient criterion for the existence of theU(1) radiation gauge in a curved space-time with isometry. This criterion is purely geometric and leads to a (local) 3+1-split of space-time with vanishing extrinsic curvature. If the symmetry is timelike and in absence of charges the generalization of the Coulomb gauge leads to a time evolution of the Maxwell field which is analogous to that in flat space-time.     

Møller Energy-Momentum Distribution of Higher Dimensional Vaidya Space-Time

In this paper, we intend to clarify the energy-momentum problem of higher dimensional Vaidya space-time in the general theory of relativity. In this connection, Møller energy and momentum for the higher dimensional Vaidya space-time are evaluated in the frame of general relativity. We have obtained that the Møller energy distribution of higher dimensional Vaidya space-time is equal to zero, while the Møller momentum distribution of higher dimensional Vaidya space-time is not equal to zero.     

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     

Theb-boundary of tensor bundles over a space-time

In [1] it was shown how to attach a boundary to any space-time. In the present paper a boundary is constructed for any bundle associated with the frame bundle of a space time. In such a way limits of tensor fields at boundary points of a space-time are defined. Using this we show that the Lorentz metric has always a unique continuous extension to theb-boundary of the space-time.Supported by Alexander von Humboldt-Stiftung.     

The Sagnac effect in curved space-times from an analogy with the Aharonov-Bohm effect

In the context of the natural splitting, the standard relative dynamics can be expressed in terms of gravito-electromagnetic fields, which allow to formally introduce a gravito-magnetic Aharonov-Bohm effect. We showed elsewhere that this formal analogy can be used to derive the Sagnac effect in flat space-time as a gravito-magnetic Aharonov-Bohm effect. Here, we generalize those results to study the General Relativistic corrections to the Sagnac effect in some stationary and axially symmetric geometries, such as the space-time around a weakly gravitating and rotating source, Kerr space-time, Gödel universe and Schwarzschild space-time.     

Null surface quantization and quantum theory of massless fields in asymptotically flat space-time

The quantum theory of massless fields in an asymptotically simple space-time is developed. The Schwinger dynamical principle and the Penrose conformal technique are exploited to derive the commutation relations on proper null surfaces in a curved space-time and on null infinities. The explicit expression for theS matrix in an asymptotically simple space-time is presented. The general expression for a density matrix describing particles created in an external field is also given and its possible applications are discussed briefly.