Towards a closed differential aging formula in special relativity

TL;DR

This paper proposes a solution for calculating differential aging in special relativity using lightlike transport, advancing the understanding of proper acceleration effects in non-inertial spacetime navigation.

Contribution

It introduces a new formula for differential aging in 3+1 dimensions based on lightlike transport, addressing a key problem in relativistic spacetime navigation.

Findings

Provides a closed-form solution for differential aging with lightlike transport.

Highlights the open problem for Fermi-Walker decomposition.

Advances tools for autonomous navigation in non-inertial frames.

Abstract

It is well known that the Lorentzian length of a timelike curve in Minkowski spacetime is smaller than the Lorentzian length of the geodesic connecting its initial and final endpoints. The difference is known as the 'differential aging' and its calculation in terms of the proper acceleration history of the timelike curve would provide an important tool for the autonomous spacetime navigation of non-inertial observers. I give a solution in 3+1 dimensions which holds whenever the acceleration is decomposed with respect to a lightlike transported frame (lightlike transport will be defined), the analogous and more natural problem for a Fermi-Walker decomposition being still open.