Phantom mass gravitational effects

TL;DR

This paper derives relativistic corrections to particle and light motion equations considering phantom mass effects in modified Newtonian gravity within Einstein's linear approximation.

Contribution

It introduces a framework for including phantom mass density in relativistic equations of motion under modified gravity theories.

Findings

Relativistic corrections to equations of motion are derived.

Phantom mass density effects are incorporated into gravitational equations.

The approach is based on Einstein's linear approximation of gravitation.

Abstract

I derive the basic relativistic corrections to the equations of motion of test particles and light rays in the field of a source with active mass $m$, including the phantom mass density that any such source generates when a modification of Newton's action at a distance includes a long range term. The technical framework of this paper is that of Einstein's theory of gravitation at the linear approximation with respect to the mass parameter $m$.