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

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.