On the Petrov classification of gravitational fields

Abstract

An intuitive directional symmetry for a null direction with respect to a given local Lorentz observer is suggested. It is shown that the existence of a null direction with such a symmetry with respect to the given Lorentz observer implies that the null direction is a Debever- Penrose direction. A weak converse is also given. In the vacuum case it is shown that the existence of such a null direction is equivalent to the space-time being algebraically special in the Petrov classification and having that null direction as a repeated principal null direction. The results are generalized to non-vacuum space-times. Finally it is suggested how a vacuum space-time might be classified according to the type of symmetries it possesses.