On the Equivalence of Gravitational Waves Formulations in Teleparallel Gravity and General Relativity

Gravitational waves have become a vital way to test our current understanding of gravity. In this work, we explore the formulations of gravitational waves in two distinct theories of gravity: the Teleparallel Equivalent of General Relativity (TEGR), a subclass of Teleparallel Gravity (TG), and General Relativity (GR). By linearizing the gravitational field equations in each theory, we demonstrate that the formulations of gravitational waves in TEGR and GR are equivalent. This equivalence suggests that the teleparallel formalism can effectively describe gravitational waves, providing a novel perspective on the topic and potentially broadening the scope of gravitational wave research.