Brian O J Tupper

General solution and classification of conformal motions in static spherical spacetimes

We find the complete and explicit general solution of the conformal Killing equation in static spherically symmetric spacetimes, thus unifying and generalizing previous special cases. For non-conformally-flat spacetimes, there are at most two proper conformal motions. There are three classes of such spacetimes, and one or both of the conformal Killing vectors is non-inheriting. One of the classes includes self-similar spacetimes (i.e. with a homothetic motion). The conformally flat spacetimes (including the Schwarzschild interior metric) fall into three classes, and their eleven proper conformal Killing vectors are given in full. The only spacetimes with conformal motion that are regular at the centre are conformally flat. An addendum for this article has been published in 1996 Class. Quantum Grav. 13 317

Spherically symmetric anisotropic fluid ICKV spacetimes

Spherically symmetric spacetimes representing an anisotropic fluid and admitting a proper inheriting conformal Killing vector (ICKV) are studied and all such spacetimes are found. It is shown that the ICKV all lie in the (t,r)-plane except in the case of those solutions that are conformally flat, in which case there exist three angular-dependent ICKV. The physical properties of these solutions are investigated (with particular attention focused on static spacetimes), and, in the context of these solutions, examples are given which can be interpreted as stellar models (with reasonable physical properties), as models of magnetic fields in a plasma, and as models of viscous heat-conducting fluids. It is shown that global monopole solutions cannot admit a proper ICKV.

Conformal motions in static spherical spacetimes

In a recent paper, we presented the general solution and classification of conformal motions in static spherically symmetric spacetimes. In this addendum, we complete the analysis by covering a degenerate case omitted in our paper.

Conformal symmetry classes for pp-wave spacetimes

We determine conformal symmetry classes for the pp-wave spacetimes. This refines the isometry classification scheme given by Sippel and Goenner (1986 Gen. Rel. Grav. 18 1229). It is shown that every conformal Killing vector for the null fluid type N pp-wave spacetimes is a conformal Ricci collineation. The maximum number of proper non-special conformal Killing vectors in a type N pp-wave spacetime is shown to be three, and we determine the form of a particular set of type N pp-wave spacetimes admitting such conformal Killing vectors. We determine the conformal symmetries of each type N isometry class of Sippel and Goenner and present new isometry classes.

A classification of spherically symmetric spacetimes

A complete classification of locally spherically symmetric four-dimensional Lorentzian spacetimes is given in terms of their local conformal symmetries. The general solution is given in terms of canonical metric types and the associated conformal Lie algebras. The analysis is based upon the local conformal decomposition into 2+2 reducible spacetimes and the Petrov type. A variety of physically meaningful example spacetimes are discussed.

Conformal symmetry inheritance in null fluid spacetimes

We define inheriting conformal Killing vectors for null fluid spacetimes and find the maximum dimension of the associated inheriting Lie algebra. We show that for non-conformally flat null fluid spacetimes, the maximum dimension of the inheriting algebra is seven and for conformally flat null fluid spacetimes the maximum dimension is eight. In addition, it is shown that there are two distinct classes of non-conformally flat generalized plane wave spacetimes which possess the maximum dimension, and one class in the conformally flat case.

The symmetries of non-null Einstein-Maxwell solutions with perfect fluid

A metric is given which contains five classes of non-null electromagnetic field plus perfect fluid solutions which possess a metric symmetry not inherited by the electromagnetic field. Two of these classes are the fluid generalisations of non-inheriting electrovac solutions given by McIntosh (1978, 1979); the others are completely new.

Killing tensors in pp-wave spacetimes

The formal solution of the second-order Killing tensor equations for the general pp-wave spacetime is given. The Killing tensor equations are integrated fully for some specific pp-wave spacetimes. In particular, the complete solution is given for the conformally flat plane wave spacetimes and we find that irreducible Killing tensors arise for specific classes. The maximum number of independent irreducible Killing tensors admitted by a conformally flat plane wave spacetime is shown to be six. It is shown that every pp-wave spacetime that admits an homothety will admit a Killing tensor of Koutras type and, with the exception of the singular scale-invariant plane wave spacetimes, this Killing tensor is irreducible.

Conformally reducible 2

Spacetimes which are conformal to 2 + 2 reducible spacetimes are considered. We classify them according to their conformal algebra, giving in each case explicit expressions for the metric and conformal Killing vectors, and providing physically meaningful examples.

plus

Spacetimes which are conformally related to reducible 1+3 spacetimes are considered. We classify these spacetimes according to the conformal algebra of the underlying reducible spacetime, giving in each case canonical expressions for the metric and conformal Killing vectors, and providing physically meaningful examples.