Szekeres-type mappings of Kasner and Petrov type I(M+) purely magnetic spacetimes

Abstract

We show that Szekeres-type mappings of Kasner spacetime generate a 2-variable Haddow magnetic spacetime of Petrov type I(M∞) and of Segré type. It is then shown that this spacetime is unique for the generating functions of 3- or 4-variable generalizations. Moreover, sufficient conditions on the variable dependence of the metric coefficients distinguishing types I(M∞) and I(M+) are established for diagonal purely magnetic spacetimes. These results are then combined by embedding the 2-variable Haddow magnetic spacetime within a diagonal spacetime such that the resulting spacetime is of Petrov type I(M+), in general. In turn, this leads to a family of non-vacuum purely magnetic spacetimes of Petrov type I(M+). It is then shown that either the anisotropic pressure tensor or heat-flux vector can be set to zero. Notably, the former class contains a sub-class of Haddow magnetic spacetimes also of Petrov type I(M+). Finally, the possibility of conformally relating the general family of non-vacuum purely magnetic spacetimes to vacuum is shown not to be possible.