Asymptotically Stationary and Static Space-times and Shear-free Null Geodesic Congruences

TL;DR

This paper explores the exact calculation of complex centers of mass and charge in asymptotically stationary or static space-times, revealing connections to gyromagnetic ratios without approximation.

Contribution

It provides an exact method for determining complex centers of mass and charge in specific space-times, extending previous approximate approaches.

Findings

Exact calculation of complex centers of mass and charge

Recovery of Dirac gyromagnetic ratio in special cases

Application to asymptotically stationary or static space-times

Abstract

In classical electromagnetic theory, one formally defines the complex dipole moment (the electric plus 'i' magnetic dipole) and then computes (and defines) the complex center of charge by transforming to a complex frame where the complex dipole moment vanishes. Analogously in asymptotically flat space-times it has been shown that one can determine the complex center of mass by transforming the complex gravitational dipole (mass dipole plus 'i' angular momentum) (via an asymptotic tetrad trasnformation) to a frame where the complex dipole vanishes. We apply this procedure to such space-times which are asymptotically stationary or static, and observe that the calculations can be performed exactly, without any use of the approximation schemes which must be employed in general. In particular, we are able to exactly calculate complex center of mass and charge world-lines for such space-times, and - as a special case - when these two complex world-lines coincide, we recover the Dirac value of the gyromagnetic ratio.