Bosonic and fermionic behavior in gravitational configurations

TL;DR

This paper extends charge quantization concepts to gravitational fields, showing that certain spacetime symmetries lead to quantization conditions and that gravitational configurations exhibit bosonic or fermionic rotational behavior.

Contribution

It introduces a method to derive quantization conditions for gravitational configurations based on spacetime symmetries and Petrov type, revealing their bosonic or fermionic nature.

Findings

Quantization conditions constrain metric parameters.

Spacetimes exhibit bosonic or fermionic rotational behavior.

Method extends charge quantization ideas to gravity.

Abstract

We extend Dirac's approach about the quantization of the electric charge to the case of gravitational configurations. The spacetime curvature is used to define a phase-like object which allows us to extract information about the behavior of the corresponding spacetime. We show that all spacetimes that satisfy certain simple symmetry condition and for which the Petrov type is the same whitin a specific region, quantization conditions can be derived that impose constraints on the possible values of the parameters entering the respective metrics. As a general result we obtain that for the gravitational configurations described by those metrics, the behavior under rotations can be only of bosonic or fermionic nature.