A Covariant Version of Verlinde's Emergent Gravity

Understand

A generally covariant version of Erik Verlinde's emergent gravity model is proposed.

• The Lagrangian constructed here allows an improved interpretation of the underlying mechanism.
• It suggests that de-Sitter space is filled with a vector-field that couples to baryonic matter and, by dragging on it, creates an effect similar to dark matter.
• We solve the covariant equation of motion in the background of a Schwarzschild space-time and obtain correction terms to the non-covariant expression.