Classical and quantum solutions of (2+1)-dimensional gravity under the de Broglie–Bohm interpretation

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 spacetime. The de Broglie–Bohm interpretation is applied to the wavefunction and we derive the differential equations for the metric. By solving these equations, we obtain the quantum effect for the metric and compare them with the classical metric. In particular, the quantum effect on the metric for the closed de Sitter universe is estimated quantitatively.