Hamilton-Jacobi Solutions for Strongly-Coupled Gravity and Matter

TL;DR

This paper develops a Green's function approach to solve strongly-coupled gravity and matter in the semiclassical limit, simplifying the equations by neglecting spatial gradients and providing exact and approximate solutions.

Contribution

It introduces a novel Green's function method for the Hamilton-Jacobi equation in the strong-coupling limit of gravity-matter systems, enabling new analytical solutions.

Findings

Exact solutions for dust and scalar fields with gravity

Approximate solutions in the strong-coupling regime

Simplified evolution equations neglecting spatial gradients

Abstract

A Green's function method is developed for solving strongly-coupled gravity and matter in the semiclassical limit. In the strong-coupling limit, one assumes that Newton's constant approaches infinity. As a result, one may neglect second order spatial gradients, and each spatial point evolves like an homogeneous universe. After constructing the Green's function solution to the Hamiltonian constraint, the momentum constraint is solved using functional methods in conjunction with the superposition principle for Hamilton-Jacobi theory. Exact and approximate solutions are given for a dust field or a scalar field interacting with gravity.