Corrections to the Newtonian Potential

Abstract

According to Newton’s law of universal gravitation, any massive object generates a gravitational potential proportional to its mass and inversely proportional to the distance to it. In this TFG we show how this Newtonian potential can be derived from the weak-field limit of Einstein’s equations. Then, we study various corrections which arise to this potential due to relativistic (controlled by 1/c), gravitational (controlled by G) and quantum effects (controlled by ℏ). We also study how the potential gets modified in the presence of extended spacetime dimensions, additional compact dimensions, as well as in the case of classical higher-curvature corrections to Einstein gravity (both with and without covariant derivatives of the Riemann tensor)