# Maximal acceleration geometries and spacetime curvature bounds

## TL;DR

This paper develops a geometric framework for maximal acceleration in spacetime, linking bounds on acceleration to bounds on curvature components, with implications for high-acceleration regimes.

## Contribution

It introduces a novel geometric approach to maximal acceleration and establishes a connection between acceleration bounds and curvature limits in spacetime.

## Key findings

- Bound on proper maximal acceleration implies bounds on Riemann curvature components.
- Framework applicable to large proper accelerations.
- Provides a geometric interpretation of acceleration limits in spacetime.

## 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 an uniform bound for certain bilinear combinations of the Riemannian curvature components in the domain of the spacetime where curvature is finite.