Theorems on Null-Paths and Red-Shift

TL;DR

This paper proves new theorems on null-paths within absolute parallelism geometry and derives a comprehensive red-shift formula applicable to cosmological and astrophysical contexts, incorporating various physical effects.

Contribution

It introduces theorems on null-paths in absolute parallelism geometry and derives a novel red-shift formula that includes gravitational, motion, spin, and line-of-sight effects.

Findings

Red-shift formula applicable to cosmological and astrophysical observations.

Theorems on null-paths in absolute parallelism geometry.

The formula reduces to known results under specific conditions.

Abstract

In the present work, we prove the validity of two theorems on null-paths in a version of absolute parallelism geometry. A version of these theorems has been originally established and proved by Kermak, McCrea and Whittaker (KMW) in the context of Riemannian geometry. The importance of such theorems is their use, in applications, to derive a general formula for the red-shift of spectral lines coming from distant objects. The formula derived in the present work, can be applied for both cosmological and astrophysical red-shifts. It takes into account the shifts resulting from gravitation, different motions of the source of photons, spin of the moving particle (photons) and the direction of the line of sight. It is shown that this formula cannot be derived in the context of Riemannian geometry, but it can be reduced to a formula given by KMW under certain conditions.