The gravitation energy–momentum pseudotensor: The cases of F(R) and F(T) gravity

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  • Salvatore Capozziello
    Dipartimento di Fisica “E. Pancini”, Università di Napoli “Federico II”, Complesso Università di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy
  • Maurizio Capriolo
    Dipartimento di Matematica Università di Salerno, via Giovanni Paolo II, 132, Fisciano, SA I-84084, Italy
  • Maria Transirico
    Dipartimento di Matematica Università di Salerno, via Giovanni Paolo II, 132, Fisciano, SA I-84084, Italy

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<jats:p> We derive the gravitational energy–momentum pseudotensor [Formula: see text] in metric [Formula: see text] gravity and in teleparallel [Formula: see text] gravity. In the first case, [Formula: see text] is the Ricci curvature scalar for a torsionless Levi-Civita connection; in the second case, [Formula: see text] is the curvature-free torsion scalar derived by tetrads and Weitzenböck connection. For both classes of theories the continuity equations are obtained in presence of matter. [Formula: see text] and [Formula: see text] are non-equivalent, but differ for a quantity [Formula: see text] containing the torsion scalar [Formula: see text] and a boundary term [Formula: see text]. It is possible to obtain the field equations for [Formula: see text] and the related gravitational energy–momentum pseudotensor [Formula: see text]. Finally we show that, thanks to this further pseudotensor, it is possible to pass from [Formula: see text]–[Formula: see text] and vice versa through a simple relation between gravitational pseudotensors. </jats:p>

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