On the fundamental groups of space-times in general relativity

It is shown that there are upper bounds on the first and second betti numbers of compact space-times or space-times with Cauchy surfaces whose fundamental groups are abelian. Homological classifications of compact space-times and space-times with compact Cauchy surfaces are given.     

Spherically symmetric space-times transparent to scalar multipole waves

Using nonscattering potentials of Chang and Janis, a large class of spherically symmetric space-times is constructed on which all multipole solutions to the minimally coupled scalar wave equation are expressible in terms of characteristic data functions in essentially as simple a fashion as for flat space-time. The space-times are transparent to multipole waves in the same sense that flat space-time is. Both conformally flat and not conformally flat space-times are obtained. Some examples are discussed which show that the variety of transparent space-times is large even within the class of Robertson-Walker spaces.     

Conformal Killing vectors and FRW spacetimes

Fluid space-times which admit a conformal Killing vector (CKV) are studied. It is shown that even in a perfect fluid space-time a conformal motion will not, in general, map the fluid flow lines onto fluid flow lines; consequently, perfect fluid space-times and, in particular, the simplest perfect fluid space-times known to admit a CKV, namely the Friedmann-Robertson-Walker (FRW) space-times, are studied. A direct proof that there do not exist any special CKV in FRW space-times will be given, thereby motivating the study of the physically more relevant proper CKV. Indeed, one of the principal motivations of the present work is the study of the symmetry inheritance problem for proper CKV. Since the FRW metric can, in general, satisfy the Einstein field equations for a non-comoving imperfect fluid, the relationship between the FRW models (and in particular the standard comoving perfect fluid models) and the conditions under which conformal motions (and in addition homothetic motions) map fluid flow lines onto fluid flow lines are investigated. Finally, further properties of fluid space-times which admit a proper CKV, and in particular space-times in which the CKV is parallel to the fluid four-velocity, are discussed.     

Ghost neutrinos as test fields in curved space-time

Without restricting to empty space-times, it is shown that ghost neutrinos (their energy-momentum tensor vanishes) can only be found in algebraically special space-times with a neutrino flux vector parallel to one of the principal null vectors of the conformal tensor. The optical properties are studied. There are no ghost neutrinos in the Kerr-Newman and in spherically symmetric space-times. The example of a non-vacuum gravitational pp-wave accompagnied by a ghost neutrino pp-wave is discussed.     

Neutrino radiation fields in general relativity

All space-times admitting a neutrino radiation field are obtained. Three classes of such space-times exist, characterised by the Weyl tensor being of type D, N (or O) or III.     

Vorticity- and shear-free space-time in general relativity

The paper studies the vorticity- and shear-free nonstatic space-times with perfect fluid source in genera] relativity and finds that such space-times are either spherically symmetric or pseudospherical or plane symmetric.     

On certain timelike symmetry properties and the evolution of matter field space-times that admit them

This paper treats matter field space-times admitting timelike conformai motions and timelike members of the family of contracted Ricci collineations (FCRC). The physical properties of these timelike symmetries in relation to the time development of relativistic matter field space-times are developed in terms of a number of specific theorems. Insofar as possible, the similarities and differences of the timelike conformal motions and the FCRC are discussed in some detail. Special applications are given that illustrate the possible value of the present considerations and related conservation expressions in relation to the Cauchy problem of matter field space-times admitting timelike symmetry properties.     

Conformally flat space-times of locally constant connection. I

Conformally flat space-times of locally constant connection are studied. The constant connection defines a global vector field which is assumed timelike. The general solution of the geodesic equations is presented and several theorems characterizing the geometry of such space-times are proved.     

Killing-Yano tensors in general relativity

It is shown that space-times admitting more than one independent Killing-Yano tensor belong to a small collection of highly idealised space-times. A new characterization of Robertson-Walker space-times arises as a corollary of the main theorem.     

Simply-transitive homothety groups

In this paper the spin-coefficient formalism of Penrose and Rindler is applied to the problem of finding space-times that admit a simply-transitive group of homotheties. The method is illustrated by an application to algebraically special vacuum space-times. Vacuum metrics with a fivedimensional homothety group are also considered.     

The equivalence of perfect fluid space-times and viscous magnetohydrodynamic space-times in general relativity

The work of a previous article [1] is extended to show that space-times which are the exact solutions of the field equations for a perfect fluid also may be exact solutions of the field equations for a viscous magnetohydrodynamic fluid. Conditions are found for this equivalence to exist and viscous magnetohydrodynamic solutions are found for a number of known perfect fluid space-times.     

Symmetry mappings in Einstein-Maxwell space-times

General properties of Einstein-Maxwell spaces, with both null and nonnull source-free Maxwell fields, are examined when these space-times admit various kinds of symmetry mappings. These include Killing, homothetic and conformal vector fields, curvature and Ricci collineations, and mappings belonging to the family of contracted Ricci collineations. In particular, the behavior of the electromagnetic field tensor is examined under these symmetry mappings. Examples are given of such space-times which admit proper curvature and proper Ricci collineations. Examples are also given of such space-times in which the metric tensor admits homothetic and other motions, but in which the corresponding Lie derivatives of the electromagnetic Maxwell tensor are not just proportional to the Maxwell tensor.On leave from Mathematics Department, Monash University, Clayton, Victoria, 3168, Australia.     

Stationary vacuum fields with a conformally flat three-space. III. Complete solution

It is shown that stationary vacuum space-times having a conformally flat 3-space are always characterized by a functional relationship between the real and imaginary parts of the Ernst potential. This result is based on a new formulation of Einstein's equation, and it completes the investigation of vacuum space-times with conformally flat spaces.     

Energy and Momentum of Robinson-Trautman Space-Times

Robinson and Trautman space-times are studied in the context of teleparallel equivalent of general relativity (TEGR). These space-times are the simplest class of asymptotically flat geometries admitting gravitational waves. We calculate the total energy for such space-times using two methods, the gravitational energy-momentum and the translational momentum 2-form. The two methods give equal results of these calculations. We show that the value of energy depends on the gravitational mass M, the Gaussian curvature of the surfaces λ(u,θ) and on the function K(u,θ). The total energy reduces to the energies of Schwarzschild’s and Bondi’s space-times under specific forms of the function K(u,θ).     

On the algebraic structure of second order symmetric tensors in 5-dimensional space-times

A new approach to the algebraic classification of second order symmetric tensors in 5-dimensional space-times is presented. The possible Segre types for a symmetric two-tensor are found. A set of canonical forms for each Segre type is obtained. A theorem which collects together some basic results on the algebraic structure of the Ricci tensor in 5-dimensional space-times is also stated.     

半平面对称非类光电磁场产生的半平面对称时空

本文通过严格求解Einatein-Maxwell场方程,找到了由半平面对称非类光电磁场产生的半平面对称静态通解,并证明此类时空只具有(?/?x)^a,(?/?y)^a和(?/?t)^a三个Killing矢量场,本文还研究了时空奇异性,证明这类时空都是测地不完备的,且所有不完备测地线都对应着Scalar Polynomial曲率奇异性. 关键词：     

Occurrence of whimper singularities

HOmogeneous space-times (i.e. those admitting a three-parameter group of isometries) are studied using the Newman Penrose formalism. It is found that solutions containing horizons depend on two fewer parameters than the most general solution, so that horizons and the associated whimper singularities are not stable features of homogeneous space-times. In the vacuum case, there are just three two-parameter families with horizons, two of which are the NUT solutions and certain plane waves.