Non-Null Torus Knotted Gravitational Waves from Gravitoelectromagnetism

TL;DR

This paper constructs a novel non-null torus-knotted gravitational wave solution using the gravitoelectromagnetic framework, analyzing its geometric properties and inherent duality and helicity features.

Contribution

It introduces the first non-null torus-knotted gravitational wave solution derived from linearized Einstein equations via GEM analogy.

Findings

Derived the line element and curvature tensors for the solution

Identified dual GEM potential and GEM helicity properties

Analyzed the geodesic equations in this background

Abstract

In this paper, we construct a non-null torus-knotted gravitational monochromatic wave solution of the linearized Einstein equations in vacuum, employing the gravitoelectromagnetic (GEM) framework by analogy with classical electrodynamics. We derive the geometric objects, including the line element, the Riemann tensor, the Ricci tensor, the Ricci scalar, and the geodesic equation for this background. Also, we investigate two properties inherent to this solution due to its GEM origin: the dual GEM potential and GEM helicity.