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

## TL;DR

This paper introduces a Ricci-type flow on the Riemannian leaf of a null manifold and establishes new gradient estimates, contributing to the geometric analysis of horizons in black hole physics.

## Contribution

It defines a novel degenerate Ricci-type flow on null manifolds and proves new gradient estimates, advancing the understanding of geometric flows in degenerate settings.

## Key findings

- Established gradient estimates for the Ricci-type flow.
- Linked the flow's behavior to geometric properties of black hole horizons.
- Provided tools for further analysis of null manifold geometries.

## Abstract

Locally, a screen integrable globally null manifold $M$ splits through a Riemannian leaf $M'$ of its screen distribution and a null curve $\mathcal{C}$ 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 degenerate Ricci-type flow in $M'$ via the intrinsic Ricci tensor of $M$. Several new gradient estimates regarding the flow are proved.