The topological pressure of trapped sets in Kerr-(de Sitter) spacetimes

TL;DR

This paper establishes that the topological pressure of normally hyperbolic trapped sets in Kerr-(de Sitter) spacetimes is negative, linking hyperbolic dynamics with geometric properties of black hole spacetimes.

Contribution

It proves the negativity of topological pressure for normally hyperbolic trapping, connecting hyperbolic dynamics with geometric analysis in Kerr-(de Sitter) spacetimes.

Findings

Topological pressure of trapped sets is negative in these spacetimes.

Connects hyperbolic dynamics with geometric properties of black holes.

Provides a bridge between low-regularity hyperbolic systems and unconditional results.

Abstract

In this paper we prove that the topological pressure of dynamic systems with normally hyperbolic trapping is negative. In particular, this applies to the null geodesic flow in Kerr and Kerr-de Sitter spacetimes This builds connection between results for trapped sets with low regularity in hyperbolic dynamic systems conditioning on negativity of the topological pressure and unconditional results in the setting of normally hyperbolic trapping.