Topological quantization of gravitational fields as generalized harmonic maps

TL;DR

This paper applies topological quantization to gravitational fields represented as generalized harmonic maps, revealing incompatibilities between classical descriptions and parameter discretization.

Contribution

It introduces a novel approach using generalized harmonic maps for gravitational fields and explores their topological quantization.

Findings

Classical gravitational fields are incompatible with parameter discretization.

Generalized harmonic maps extend harmonic map concepts to Einstein solutions.

Results suggest limitations of classical symmetry descriptions in quantum regimes.

Abstract

We apply the topological quantization method to some gravitational fields which can be represented as generalized harmonic maps. This representation extends the well-known concept of harmonic maps and allows us to describe some solutions to the Einstein field equations as generalized strings, where the base space for the generalized harmonic map is a two-dimensional manifold. The results obtained here point to an incompatibility of the classical description of the gravitational field and its symmetries with a discretization of the parameters that enter in its description.