The gravitational energy-momentum pseudo-tensor in $f(Q)$ non-metric gravity
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arXiv
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| Format: | Preprint |
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2026
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| author | Capozziello, Salvatore Capriolo, Maurizio Lambiase, Gaetano |
| author_facet | Capozziello, Salvatore Capriolo, Maurizio Lambiase, Gaetano |
| contents | We derive the affine tensor associated with the energy and momentum densities of both gravitational and matter fields, the complex pseudo-tensor, for $f(Q)$ non-metric gravity, the straightforward extension of Symmetric Teleparallel Equivalent of General Relativity (STEGR), characterized by a flat, torsion-free, non-metric connection. The local conservation of energy-momentum complex on-shell is satisfied through a continuity equation. An important analogy is pointed out between gravitational pseudo-tensor of teleparallel $f(T)$ gravity, in the Weitzenböck gauge, and the same object of symmetric teleparallel $f(Q)$ gravity, in the coincident gauge. Furthermore, we perturb the gravitational pseudo-tensor $τ^α_{\phantomαλ}$ in the coincident gauge up to the second order in the metric perturbation, obtaining a useful expression for the power carried by the related gravitational waves. We also present an application of the gravitational pseudotensor, determining the gravitational energy density of a Schwarzschild spacetime in STEGR gravity, adopting the concident gauge. Finally, analyzing the conserved quantities on manifolds, the Stokes theorem can be formulated for generic affine connections |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_12088 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The gravitational energy-momentum pseudo-tensor in $f(Q)$ non-metric gravity Capozziello, Salvatore Capriolo, Maurizio Lambiase, Gaetano General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory We derive the affine tensor associated with the energy and momentum densities of both gravitational and matter fields, the complex pseudo-tensor, for $f(Q)$ non-metric gravity, the straightforward extension of Symmetric Teleparallel Equivalent of General Relativity (STEGR), characterized by a flat, torsion-free, non-metric connection. The local conservation of energy-momentum complex on-shell is satisfied through a continuity equation. An important analogy is pointed out between gravitational pseudo-tensor of teleparallel $f(T)$ gravity, in the Weitzenböck gauge, and the same object of symmetric teleparallel $f(Q)$ gravity, in the coincident gauge. Furthermore, we perturb the gravitational pseudo-tensor $τ^α_{\phantomαλ}$ in the coincident gauge up to the second order in the metric perturbation, obtaining a useful expression for the power carried by the related gravitational waves. We also present an application of the gravitational pseudotensor, determining the gravitational energy density of a Schwarzschild spacetime in STEGR gravity, adopting the concident gauge. Finally, analyzing the conserved quantities on manifolds, the Stokes theorem can be formulated for generic affine connections |
| title | The gravitational energy-momentum pseudo-tensor in $f(Q)$ non-metric gravity |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.12088 |