We consider a general class of four-dimensional geometries admitting a null vector field that has no twist

and no shear but has an arbitrary expansion. We explicitly present the Petrov classification of such

Robinson-Trautman (and Kundt) gravitational fields, based on the algebraic properties of the Weyl tensor.

In particular, we determine all algebraically special subcases when the optically privileged null vector field

is a multiple principal null direction (PND), as well as all the cases when it remains a single PND. No field

equations are a priori applied, so that our classification scheme can be used in any metric theory of gravity

in four dimensions. In the classic Einstein theory, this reproduces previous results for vacuum spacetimes,

possibly with a cosmological constant, pure radiation, and electromagnetic field, but can be applied to an

arbitrary matter content. As nontrivial explicit examples, we investigate specific algebraic properties of the

Robinson-Trautman spacetimes with a free scalar field, and also black hole spacetimes in the pure Einstein-

Weyl gravity.

and no shear but has an arbitrary expansion. We explicitly present the Petrov classification of such

Robinson-Trautman (and Kundt) gravitational fields, based on the algebraic properties of the Weyl tensor.

In particular, we determine all algebraically special subcases when the optically privileged null vector field

is a multiple principal null direction (PND), as well as all the cases when it remains a single PND. No field

equations are a priori applied, so that our classification scheme can be used in any metric theory of gravity

in four dimensions. In the classic Einstein theory, this reproduces previous results for vacuum spacetimes,

possibly with a cosmological constant, pure radiation, and electromagnetic field, but can be applied to an

arbitrary matter content. As nontrivial explicit examples, we investigate specific algebraic properties of the

Robinson-Trautman spacetimes with a free scalar field, and also black hole spacetimes in the pure Einstein-

Weyl gravity.

typ: | article |
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journal: | Phys. Rev. D |

volume: | 94 |

pages: | 063043 |

year: | 2016 |