Conical Singular Solutions in (2+1)-Dimensional Gravity Employing the ADM Canonical Formalism

TL;DR

This paper investigates conical singularities in (2+1)-dimensional gravity using the ADM formalism, revealing topological defects in closed de Sitter universes and analyzing quantum effects via the de Broglie-Bohm interpretation.

Contribution

It introduces a detailed analysis of conical singularities in (2+1)D gravity and explores quantum tunneling effects on these singularities within the ADM framework.

Findings

Conical singularities appear as topological defects in closed de Sitter universes.

Quantum tunneling effects are finite for closed universes.

No quantum effects are observed for open universes.

Abstract

Topological solutions in the (2+1)-dimensional Einstein theory of gravity are studied within the ADM canonical formalism. It is found that a conical singularity appears in the closed de Sitter universe solution as a topological defect in the case of the Einstein theory with a cosmological constant. Quantum effects on the conical singularity are studied using the de Broglie-Bohm interpretation. Finite quantum tunneling effects are obtained for the closed de Sitter universe, while no quantum effects are obtained for an open universe.