Energy and entropy in the Geometrical Trinity of gravity

Abstract: All energy is gravitational energy. That is the consequence of the equivalence principle, according to which gravity is the universal interaction. The physical charges of this interaction have remained undisclosed, but the Adventof the Geometrical Trinity opened a new approach to this foundational problem. Here it is shown to provide a background-independent unification of the previous, non-covariant approaches of Bergmann-Thomson, Cooperstock, Einstein, von Freud, Landau-Lifshitz, Papapetrou and Weinberg. First, the Noether currents are derived for a generic Palatini theory of gravity coupled with generic matter fields, and then the canonical i.e. the unique charges are robustly derived and analysed, particularly in the metric teleparallel and the symmetric teleparallel versions of General Relativity. These results, and their application to black holes and gravitational waves, are new.