Classical and Quantum Solutions of 2+1 Dimensional Gravity under De Broglie-Bohm Interpretation

TL;DR

This paper explores classical and quantum solutions of 2+1 dimensional Einstein gravity using the de Broglie-Bohm interpretation, deriving quantum-corrected metrics and analyzing their effects on the de Sitter universe.

Contribution

It introduces a novel application of the de Broglie-Bohm interpretation to 2+1D gravity, deriving quantum-corrected metrics and comparing them with classical solutions.

Findings

Quantum effects modify the classical metrics.

Quantitative analysis of quantum impact on de Sitter universe.

Derivation of differential equations for metrics with quantum corrections.

Abstract

We have studied classical and quantum solutions of 2+1 dimensional Einstein gravity theory. Quantum theory is defined through the local conserved angular momentum and mass operators in the case of spherically symmetric space-time. The de Broglie-Bohm interpretation is applied for the wave function and we derive the differential equations for metrics. Metrics including quantum effect are obtained in solving these equations and we compare them with classical metrics. Especially the quantum effect on the closed de Sitter universe is evaluated quantitatively.