Quantized singularities in the gravitational field

Abstract

The Cabibbo-Ferrari derivation of the Dirac charge quantization condition in electromagnetism is extended to the gravitational field. This is accomplished by use of the pathdependent formalism pioneered by Mandelstam. As a result, we find that the Bianchi identity generalizes to include a quantized, singular source term for the dual Riemann tensor. Under reasonable assumptions, this source term is proportional to the divergence of the energy-momentum tensor, leading to a quantized violation of local energy conservation. Specifically, it is found that the magnitude of the time rate of appearance of three-momentum in any volume of three-space must be an integer multiple of 3c ⁴/2G. Some physical aspects of this energy nonconservation are briefly considered.