Topological Quantum Gravity through Harmonic S${}^2$ Maps

Abstract

By virtue of harmonic maps on two-dimensional spheres (S${}^2$), a topological quantization in spacetime is proposed. The discrete character of all physical quantities follows naturally. A Schwarzschild black hole, non-black hole and wormhole based geometries are considered in which a quantum hair becomes effective. A thermometer or curvature-detecting device can record the macroscopic quantumness of spacetime.

This paper is dedicated to Prof. Metin Gürses on the occasion of his completion of sixty fruitful years of contributions to the field of General Relativity