M. P. Machado Ramos

Invariant differential operators and the Karlhede classification of type N vacuum solutions

A spacetime calculus based on a single null direction, and which is therefore invariant under null rotations, is employed to show that a type N vacuum solution of Einsteins equations requires the calculation of at most five covariant derivatives of the curvature for its complete Karlhede classification.

Obtaining a class of type N pure radiation metrics using invariant operators

We develop further the integration procedure in the generalized invariant formalism, and demonstrate its efficiency by obtaining a class of Petrov type N pure radiation metrics without any explicit integration, and with comparatively little detailed calculations. The method is similar to the one exploited by Edgar and Vickers when deriving the general conformally flat pure radiation metric. A major addition to the technique is the introduction of non-intrinsic elements in the generalized invariant formalism, which can be exploited to keep calculations manageable.

Obtaining a class of type O pure radiation metrics with a negative cosmological constant, using invariant operators

Using the generalised invariant formalism we derive a special subclass of conformally flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar component. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N, respectively. In this paper we demonstrate how to handle, in the generalised invariant formalism, spacetimes with isotropy freedom and rich Killing vector structure. Once the spacetimes have been constructed, it is straightforward to deduce their Karlhede classification: the Karlhede algorithm terminates at the fourth derivative order, and the spacetimes all have one degree of null isotropy and three, four or five Killing vectors.

Type O pure radiation metrics with a cosmological constant

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant Λ, and

Symmetries and the Karlhede classification of type N vacuum solutions

\tau \ne 0

Dynamical properties of a cosmological model with diffusion

, by considering the case

Invariant classification of metrics using invariant formalism

\Lambda +\tau\bar\tau \ne 0