Generalized Doppler effect in spaces with a transport along paths

TL;DR

This paper explores a generalized Doppler effect within manifolds equipped with a transport along paths, applicable to both massless and massive particles, extending classical understanding to more abstract geometric settings.

Contribution

It introduces a generalized Doppler effect framework in manifolds with transports along paths, broadening the classical concept to include diverse geometric structures.

Findings

Results are valid for both massless and massive particles.

The generalized Doppler effect is derived in the context of manifolds with transport along paths.

Applicable to various geometric configurations, including parallel transports.

Abstract

An analog of the classical Doppler effect is investigated in spaces (manifolds) whose tangent bundle is endowed with a transport along paths, which, in particular, can be parallel one. The obtained results are valid irrespectively to the particles mass, i.e. they hold for massless particles (e.g. photons) as well as for massive ones.