Jaume Carot

On the definition of cylindrical symmetry

The standard definition of cylindrical symmetry in general relativity is reviewed. Taking the view that axial symmetry is an essential prerequisite for cylindrical symmetry, it is argued that the requirement of orthogonal transitivity of the isometry group should be dropped, this leading to a new, more general definition of cylindrical symmetry. Stationarity and staticity in cylindrically symmetric spacetimes are then defined, and these issues are analysed in connection with orthogonal transitivity, thus proving some new results on the structure of the isometry group for this class of spacetimes.

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.

Some developments on axial symmetry

The definition of axial symmetry in general relativity is reviewed, and some results concerning the geometry in a neighbourhood of the axis are derived. Expressions for the metric are given in different coordinate systems, and emphasis is placed on how the metric coefficients tend to zero when approaching the axis. PACS numbers: 0420C, 0420J

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.

Scalar field cosmologies: a dynamical systems study

Inhomogeneous G2 solutions whose material content can be modelled by a scalar field are considered with a view towards their application as cosmological models. Some generic features of these spacetimes are reviewed and discussed, and dynamical systems theory is used to analyse the qualitative behaviour of this class of spacetimes; giving special attention to the equilibrium (fixed) points of the dynamical system and their associated metrics, and discussing their inflationary behaviour.

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

It is shown that, given an analytic Lorentzian metric on a 4-manifold, gab, which admits two Killing vector fields, there exists a local deformation law ηab = a gab + b Hab, where Hab is a two-dimensional projector, such that ηab is flat and admits the same Killing vectors. We also characterize the particular case when the projector Hab coincides with the quotient metric. We apply some of our results to general stationary axisymmetric spacetimes.

2 spacetimes

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.

Flat deformation of a spacetime admitting two commuting Killing fields

Scalar field spacetimes are considered with a view towards their applications in cosmology. Some results existing in the literature are reviewed and some new results are proved concerning scalar field spacetimes in general and inhomogeneous G2 cosmological models in particular.

Conformally reducible 1+3 spacetimes

It is shown that, given an analytic Lorentzian metric on a 4-manifold, gab, which admits two Killing vector fields, it exists a local deformation law ηab = agab + b Hab, where Hab is a 2-dimensional projector, such that ηab is flat and admits the same Killing vectors.