Quantum corpuscular corrections to the Newtonian potential

Understand

We study an effective quantum description of the static gravitational potential for spherically symmetric systems up to the first post-Newtonian order.

• We start by obtaining a Lagrangian for the gravitational potential coupled to a static matter source from the weak field expansion of the Einstein-Hilbert action.
• By analysing a few classical solutions of the resulting field equation, we show that our construction leads to the expected post-Newtonian expressions.
• Next, we show that one can reproduce the classical Newtonian results very accurately by employing a coherent quantum state and modifications to include the first post-Newtonian corrections are considered.