Seminário no dia 01/10 às 10h

Abstract: We have recently presented for the first time a pair of null coordinates in Kerr spacetime, which are naturally adapted to the horizons and future null infinity. We will show that they can be generated by the congruence of null geodesics that are orthogonal to the center of mass sections at future null infinity. These null coordinates define a smooth round family of null hypersurfaces which foliate the Kerr spacetime, in an outgoing and ingoing sense respectively and have a regular extension to the horizons. Because of Kerr's peculiar geometry, the construction involves a non-linear differential equation; which is difficult to solve by traditional analytic methods, and its solution can not be expressed in terms of simple analytic functions. We solve it numerically. In this setting there naturally appears a family of spheres that are parameterized by $r_s$, which are the intersections of both null coordinates, and $r_s$ can be thought as the tortoise coordinate extension for the Kerr space-time. We use this construction to tackle the problem of the global causal structure of Kerr spacetime; which is the subject of the last part of our talk.