K\"ahler metrics via Lorentzian Geometry in dimension four

Given a semi-Riemannian $4$-manifold $(M,g)$ with two distinguished vector fields satisfying properties determined by their shear, twist and various Lie bracket relations, a family of K\"ahler metrics $g_K$ is constructed, defined on an open set in $M$, which coincides with $M$ in many typical examples. Under certain conditions $g$ and $g_K$ share various properties, such as a Killing vector field or a vector field with a geodesic flow. In some cases the K\"ahler metrics are complete. The Ricci and scalar curvatures of $g_K$ are computed under certain assumptions in terms of data associated to $g$. Many examples are described, including classical spacetimes in warped products, for instance de Sitter spacetime, as well as gravitational plane waves, metrics of Petrov type $D$ such as Kerr and NUT metrics, and metrics for which $g_K$ is an SKR metric. For the latter an inverse ansatz is described, constructing $g$ from the SKR metric.Comment: This version contains minor additions: Sec. 4.4, and further material on completeness (sec. 9.5). A sequel arXiv:1811.08999 contains K\"ahler-Einstein and other metrics obtained by the constructio

Credible Equilibria in Games with Utility Changing during the Play

Publicado por Tilburg Center Economic Research 1992Whenever one deals with an interactive decision situation of long duration, one has to take into account that priorities of the participants may change during the conflicto In this paper we propose an extensiveform game model to handle such situations and suggest and study a solution concept, called credible equilibrium, which generalizes the concept of Nash equilibrium. We also discuss possible variants to this concept and applications of the model to other types of games