Relativistic MOND from Modified Energetics

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.

arXiv comment7pp

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• A relativistic description of MOND using the Palatini formalism in an extended metric theory of gravity
• The Radial Acceleration Relation and a Magnetostatic Analogy in Quasilinear MOND
• Dynamics of clusters of galaxies with extended $f(\chi )$ gravity