Relativistic MOND from Modified Energetics

TL;DR

This paper explores how modifying the energy-momentum tensor can produce a relativistic version of MOND, extending Milgrom's approach without relying on an action principle, and ensuring conservation in different regimes.

Contribution

It introduces a novel modification to the energy-momentum tensor involving the metric determinant, enabling a proper relativistic MOND limit without an explicit action.

Findings

Proper MOND limit achieved with modified energy-momentum tensor

Conservation of energy-momentum tensor in Newtonian and MOND regimes

Extension of Milgrom's modified inertia to relativistic domain

Abstract

We begin to investigate the question of what modifications in energy-momentum tensor can yield correct MOND regime. As a starting study, we refrain from insisting on an action principle and focus exclusively on the equations of motion. The present work, despite the absence of an explicit action functional, can be regarded to extend Milgrom's modified inertia approach to relativistic domain. Our results show that a proper MOND limit arises if energy-momentum tensor is modified to involve determinant of the metric tensor in reference to the flat metric, where the latter is dynamically generated as in gravitational Higgs mechanism. This modified energy-momentum tensor is conserved in both Newtonian and MONDian regimes.