Probing Quantum Gravity Through Exactly Soluble Midi-Superspaces I

TL;DR

This paper investigates the quantization of a simplified model of quantum gravity derived from Einstein-Rosen solutions, addressing boundary conditions and regularization, to explore fundamental issues in quantum gravity.

Contribution

It provides a detailed analysis of the quantum theory of midi-superspaces related to Einstein-Rosen solutions, highlighting new insights into boundary conditions and regularization techniques.

Findings

Clarified the role of asymptotically flat boundary conditions in quantum gravity.

Identified and addressed functional analytic subtleties in regularization.

Provided a framework for analyzing conceptual issues in quantum gravity.

Abstract

It is well-known that the Einstein-Rosen solutions to the 3+1 dimensional vacuum Einstein's equations are in one to one correspondence with solutions of 2+1 dimensional general relativity coupled to axi-symmetric, zero rest mass scalar fields. We first re-examine the quanization of this midi-superspace paying special attention to the asymptotically flat boundary conditions and to certain functional analytic subtleties associated with regularization. We then use the resulting quantum theory to analyze several conceptual and technical issues of quantum gravity.