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

TL;DR

This paper proposes a topological quantization approach to spacetime using harmonic maps on S², leading to discrete physical quantities and revealing quantum features in various geometries, including black holes and wormholes.

Contribution

It introduces a novel topological quantization method based on harmonic S² maps, connecting geometry with quantum properties of spacetime.

Findings

Discrete physical quantities emerge naturally from the topological approach

Quantum hair effects are identified in black hole and wormhole geometries

Macroscopic quantumness can be detected by curvature-sensitive devices

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.