Periodic relativity: deflection of light, acceleration, rotation curves

TL;DR

This paper introduces a vectorial approach to light deflection and proposes a physical theory for galaxy rotation curves based on a second solution to Einstein's equations, offering an alternative to dark matter models.

Contribution

It presents a new relativistic framework for light deflection and galaxy rotation curves, replacing MOND with a deviation factor derived from Einstein's field equations.

Findings

Correctly predicts orbital periods of stars in galaxies.

Provides a Lorentz invariant expression for acceleration.

Offers an alternative explanation for galaxy rotation without dark matter.

Abstract

Vectorial analysis relating to derivation of deflection of light is presented. Curvilinear acceleration is distinguished from the Newtonian polar conic acceleration. The difference between the two is due to the curvature term. Lorentz invariant expression for acceleration is derived. A physical theory of rotation curves of galaxies based on second solution to Einstein's field equation is presented. Theory is applied to Milky Way, M31, NGC3198 and Solar system. Modified Kepler's third law yields correct orbital periods of stars in a galaxy. Deviation factor in the line element of the theory happens to be the ratio of the Newtonian gravitational acceleration to the measured acceleration of the star in the galaxy. Therefore this deviation factor can replace the MOND function.