Loop quantum gravity with optimal control path integral, and application to black hole tunneling

TL;DR

This paper introduces a new path integral formalism for quantum gravity based on optimal control theory, enabling analysis of black hole tunneling phenomena with a novel Lagrangian and Ashtekar variables.

Contribution

It develops a generalized path integral approach to Einstein's gravity using optimal control, leading to a new Lagrangian and applications to black hole tunneling.

Findings

Exact recovery of Einstein field equations from the new action

Formulation of quantum gravity using Ashtekar variables

Analysis of black hole tunneling in a toy model

Abstract

This paper presents a novel path integral formalism for Einstein's theory of gravitation from the viewpoint of optimal control theory. Despite its close relation to the well-known variational principles of physicists, optimal control turns out to be more general. Within this context, a Lagrangian different from the Einstein-Hilbert Lagrangian is defined. Einstein field equations are recovered exactly with variations of the new action functional. The quantum theory is obtained using Ashtekar variables and the loop scalar product. By means of example, the tunneling process of a black hole into another black hole or into a white hole is investigated with a toy model.