Classical gravitational spin-spin interaction

TL;DR

This paper presents an exact solution in Einstein's equations for two massless spinning particles, confirming the spin-spin interaction's form and its inverse fourth power dependence on distance.

Contribution

It provides the first exact, axially symmetric solution for two massless spinning particles, validating previous approximate results on spin-spin interactions.

Findings

Spin-spin force proportional to inverse fourth power of distance

Exact solution confirms approximate spin-spin interaction results

Supports theoretical models of spinning particle interactions in general relativity

Abstract

I obtain an exact, axially symmetric, stationary solution of Einstein's equations for two massless spinning particles. The term representing the spin-spin interaction agrees with recently published approximate work. The spin-spin force appears to be proportional to the inverse fourth power of the coordinate distance between the particles.