# Quantum corpuscular corrections to the Newtonian potential

## TL;DR

This paper develops a quantum effective theory of the gravitational potential that accurately reproduces classical post-Newtonian results and connects quantum corpuscular models with gravitational physics.

## Contribution

It introduces a quantum framework for the Newtonian potential incorporating first post-Newtonian corrections, linking corpuscular black hole models with classical gravity.

## Key findings

- Classical post-Newtonian expressions are recovered from the quantum model.
- Quantum coherent states can reproduce Newtonian gravity with high accuracy.
- The approach establishes a connection between quantum black hole models and classical gravitational physics.

## Abstract

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. Our findings establish a connection between the corpuscular model of black holes and post-Newtonian gravity, and set the stage for further investigations of these quantum models.