Field equations and particle motion in covariant emergent gravity

TL;DR

This paper develops the full set of field equations for covariant emergent gravity, providing solutions and analyzing particle motion, light deflection, and the role of a vector field as dark matter within this framework.

Contribution

It presents the complete covariant field equations for emergent gravity, including solutions and particle motion analysis, extending previous models with relativistic corrections.

Findings

Exact static, spherically symmetric solutions with vector fields

Relativistic test particle equations reduce to Modified Newtonian Dynamics

Vector field increases light deflection angle

Abstract

We derive the full set of field equations based on Hossenfelder's recent covariant formulation of the emergent gravity model, along with perturbative and exact solutions. The exact solution describes a static, spherically-symmetric spacetime with a non-trivial vector field which plays the role of dark matter under the emergent gravity paradigm. Equations of motion of relativistic test masses are derived and are shown to reduce to Modified Newtonian Dynamics with additional relativistic corrections. It is also shown that the presence of the vector field gives an additional positive contribution to the bending angle in the deflection of light.