Quantum post-Newtonian theory for corpuscular Black Holes

TL;DR

This paper develops a quantum effective theory for static gravitational fields incorporating post-Newtonian corrections, linking classical post-Newtonian gravity with a quantum corpuscular black hole model.

Contribution

It introduces a quantum framework for post-Newtonian gravity using a coherent state approach, connecting classical and quantum descriptions of black holes.

Findings

Classical solutions reproduce known post-Newtonian expansion.

Quantum coherent states are adapted to include post-Newtonian effects.

Establishes a theoretical link between corpuscular black holes and standard gravity.

Abstract

We discuss an effective theory for the quantum static gravitational potential in spherical symmetry up to the first post-Newtonian correction. We build a suitable Lagrangian from the weak field limit of the Einstein-Hilbert action coupled to pressureless matter. Classical solutions of the field equation lead to the correct post-Newtonian expansion. Furthermore, we portray the Newtonian results in a quantum framework by means of a coherent quantum state, which is properly corrected to accomodate post-Newtonian corrections. These considerations provide a link between the corpuscular model of Dvali and Gomez and standard post-Newtonian gravity, laying the foundations for future research.