A Ricci-type flow on globally null manifolds and its gradient estimates

Abstract

Locally, a screen integrable globally null manifold M splits through a Riemannian leaf SBS M' of its screen distribution and a null curve C' tangent to its radical distribution. The leaf M' carries a lot of geometric information about M and, in fact, forms a basis for the study of expanding and non-expanding horizons in black hole theory. In the present paper, we introduce a Ricci-typeowin M' via the intrinsic Ricci tensor of M. Several new gradients estimates regarding the how are proved.