An Einstein-like theory of gravity with a non-newtonian weak-field limit

Abstract

We propose a model describing Einstein gravity coupled to a scalar field with an exponential potential. We show that the weak-field limit of the model has static solutions given by a gravitational potential behaving for large distances as \ln r . The Newtonian term GM/r appears only as subleading. Our model can be used to give a phenomenological explanation of the rotation curves of the galaxies without postulating the presence of dark matter. This can be achieved only by giving up at galactic scales Einstein equivalence principle.

Final version, accepted for publication on General Relativity and Gravitation

References in corpus (2)

• Quintessence arising from exponential potentials
• On the Space Time of a Galaxy

Cited by in corpus (6)

• Field-theoretical formulations of MOND-like gravity
• The Pioneer Anomaly
• Insight into the baryon-gravity relation in galaxies
• Galactic orbital motions in the Dark Matter, MOdified Newtonian Dynamics and MOdified Gravity scenarios
• Black hole solutions of gravity theories with nonminimal coupling between matter and curvature
• General models of Einstein gravity with a non-Newtonian weak-field limit