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- Title
The gravitation energy–momentum pseudotensor: The cases of F(R) and F(T) gravity.
- Authors
Capozziello, Salvatore; Capriolo, Maurizio; Transirico, Maria
- Abstract
We derive the gravitational energy–momentum pseudotensor τ λ σ in metric f (R) gravity and in teleparallel f (T) gravity. In the first case, R is the Ricci curvature scalar for a torsionless Levi-Civita connection; in the second case, T 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. f (R) and f (T) are non-equivalent, but differ for a quantity ω (T , B) containing the torsion scalar T and a boundary term B. It is possible to obtain the field equations for ω (T , B) and the related gravitational energy–momentum pseudotensor τ λ σ | ω. Finally we show that, thanks to this further pseudotensor, it is possible to pass from f (R) – f (T) and vice versa through a simple relation between gravitational pseudotensors.
- Subjects
GRAVITATION; LEVI-Civita tensor; ENERGY momentum relationship; GRAVITY; BOUNDARY value problems
- Publication
International Journal of Geometric Methods in Modern Physics, 2018, Vol 15, pN.PAG
- ISSN
0219-8878
- Publication type
Article
- DOI
10.1142/S0219887818501645