Towards testing a dark matter candidate that emerges from the scalar ether theory

Mayeul Arminjon (1)

1 3SR - Laboratoire sols, solides, structures - risques [Grenoble]

According to a scalar theory of gravity with a preferred frame, electromagnetism in the presence of a gravitational field implies that there is an additional energy tensor, which might contribute to dark matter. The expression of this tensor is determined by a mere scalar p, that depends on the EM field and (for a weak field) on the Newtonian gravitational field. We briefly recall why this tensor arises and how the EM field in a galaxy can be calculated. The data fields that enter the PDE for the scalar field p oscillate very quickly in space and time, as does the EM field. This prevents to integrate that PDE at the relevant galactic scale. Therefore, a homogenization of that PDE has to be operated. We discuss in some detail three possible ways of applying the homogenization theory to that PDE: time, space, or spacetime homogenization. The second and third ways may lead to feasible, albeit heavy calculations.

Mots clés: Dark matter; homogenization theory; Maxwell equations; alternative theory of gravity

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]; Physique mathématique [math-ph]

Mayeul Arminjon. Towards testing a dark matter candidate that emerges from the scalar ether theory. 2022. ⟨hal-03826319v1⟩