Conformal Patterson-Walker metrics
  The classical Patterson-Walker construction of a split-signature (pseudo-)Riemannian structure from a given torsion-free affine connection is generalized to a construction of a split-signature conformal structure from a given projective class of connections. A characterization of the induced structures is obtained. We achieve a complete description of Einstein metrics in the conformal class formed by the Patterson-Walker metric. Finally, we describe all symmetries of the conformal Patterson-Walker metric. In both cases we obtain descriptions in terms of geometric data on the original structure. 
Matthias Hammerl, Katja Sagerschnig, Josef \v{S}ilhan, Arman   Taghavi-Chabert and Vojt\v{e}ch \v{Z}\'adn\'ik
math.DG gr-qc hep-th math-ph math.MP