English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We derive the gravitational energy-momentum pseudotensor $ \tau^{\sigma}_{\phantom {\sigma} \lambda} $ in metric $ f\left (R \right) $ gravity and inteleparallel $ f\left (T\right) $ gravity. In the first case, $R$ is the Riccicurvature scalar for a torsionless Levi-Civita connection; in the second case,$T$ is the curvature-free torsion scalar derived by tetrads and Weitzenb\"ockconnection. For both classes of theories the continuity equations are obtainedin presence of matter. $ f \left (R \right) $ and $ f \left (T \right) $ arenon-equivalent but differ for a quantity $ \omega \left (T, B \right) $containing the torsion scalar $T$ and a boundary term $ B $. It is possible toobtain the field equations for $ \omega \left (T, B \right) $ and the relatedgravitational energy-momentum pseudotensor $ \tau^{\sigma}_{\phantom{\sigma}\lambda} \vert \omega $. Finally we show that, thanks to this furtherpseudotensor, it is possible to pass from $ f \left (R \right) $ to $ f \left (T \right) $ and viceversa through a simple relation between gravitationalpseudotensors.

The gravitational energy-momentum pseudotensor: the cases of $f(R)$ and $f(T)$ gravity