  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.
