Tidal tensors in the description of gravity and electromagnetism

TL;DR

This paper explores a unified mathematical framework using tangent bundle connections to describe gravity and electromagnetism through tidal tensors, enhancing the gravito-electromagnetic analogy.

Contribution

It introduces a covariant geometrization of tidal tensor-based gravito-electromagnetic equations using tangent bundle connections.

Findings

Unified geometric description of gravity and electromagnetism

Enhanced understanding of tidal tensor roles in both theories

Potential for new insights into gravito-electromagnetic phenomena

Abstract

In 2008-2009, F. Costa and C. Herdeiro proposed a new gravito-electromagnetic analogy, based on tidal tensors. We show that connections on the tangent bundle of the space-time manifold can help not only in finding a covnenient geometrization of their ideas, but also a common mathematical description of the main equations of gravity and electromagnetism.