Topological quantization of gravitational fields

TL;DR

This paper develops a topological quantization method for gravitational fields, demonstrating that parameters in various solutions like black holes and monopoles satisfy specific discretization conditions.

Contribution

It systematically introduces topological quantization for gravity, extending to gauge matter fields and providing explicit examples with quantization conditions.

Findings

Parameters in gravitational solutions are discretized by topological quantization.

Applicable to vacuum and matter-coupled Einstein solutions.

Includes examples like black holes and monopoles.

Abstract

We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes values in the Lie algebra of the Lorentz group. This result is generalized to include the case of gauge matter fields in multiple principal fiber bundles. We present several examples of gravitational configurations that include a gravitomagnetic monopole in linearized gravity, the C-energy of cylindrically symmetric fields, the Reissner-Nordstr\"om and the Kerr-Newman black holes. As a result of the application of the topological quantization procedure, in all the analyzed examples we obtain conditions implying that the parameters entering the metric in each case satisfy certain discretization relationships.