Maximal acceleration geometries and spacetime curvature bounds

Abstract

A geometric framework for metrics of maximal acceleration which is applicable to large proper accelerations is discussed, including a theory of connections associated with the geometry of maximal acceleration. In such a framework, it is shown that the uniform bound on the proper maximal acceleration implies a uniform bound for certain bilinear combinations of the Riemannian curvature components in the domain of the spacetime where curvature is finite.