MOND formulation emerging from general relativity

In this paper, we demonstrate that the effects of Dark-Matter, partially in the way proposed by the Modified Newtonian Dynamics (MOND), emerge naturally from the standard theory of General Relativity (without any modification) under a new proposed vacuum solution. There is a family of metric solutions able to reproduce the galaxy rotation curves and the relevant scales where the Dark-Matter effects are supposed to appear in a galaxy. This family of solutions deviate from the standard spherically symmetric solution. The proposed formulation, being relativistic by nature, opens the scenario where we can test the relativistic effects attributed to Dark-Matter and having relevance in cosmology. Among such effects, we have gravitational lensing, effects on the CMB scenario and effects on the formation of galaxies.