The gravitational energy-momentum pseudo-tensor in $f(Q)$ non-metric gravity

Abstract

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 ${\tau }_{\lambda }^{\alpha }$ 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

arXiv comment24 pages, accepted for publication on Phys. Rev. D

References in corpus (39)

• Cosmology in $f(Q)$ geometry
• $f(Q,T)$ gravity
• Coupling matter in modified $Q$-gravity
• Covariant conservation of energy momentum in modified gravities
• Teleparallel Palatini theories
• Modified Gravity and Cosmology: An Update by the CANTATA Network
• Black holes in $f(\mathbb{Q})$ Gravity
• Comparing Equivalent Gravities: common features and differences
• Polarization of gravitational waves in symmetric teleparallel theories of gravity and their modifications
• Energy-Momentum Conservation in General Relativity
• Propagation of gravitational waves in symmetric teleparallel gravity theories
• Energy-Momentum Complex in Møller's Tetrad Theory of Gravitation
• Slow-roll inflation in $f(Q)$ non-metric gravity
• Weak Field Limit and Gravitational Waves in $f(T,B)$ Teleparallel Gravity
• On the impact of $f(Q)$ gravity on the Large Scale Structure
• Non-metricity with bounday terms: $f(Q,C)$ gravity and cosmology
• Family of scalar-nonmetricity theories of gravity
• Quasinormal Modes of Black holes in $f(Q)$ gravity
• Energy-momentum complexes in f(R) theories of gravity
• The gravitational energy-momentum pseudotensor: the cases of $f(R)$ and $f(T)$ gravity
• Coincident f(Q) gravity: black holes, regular black holes and black bounces
• Coincident gauge for static spherical field configurations in symmetric teleparallel gravity
• Data reconstruction of the dynamical connection function in $f(Q)$ cosmology
• Considerations on gravitational waves in higher-order local and non-local gravity
• The gravitational energy-momentum pseudo-tensor of Higher-Order Theories of Gravity
• Observational test for $f(Q)$ gravity with weak gravitational lensing
• Non-metric chaotic inflation
• Weak field limit and gravitational waves in higher-order gravity
• Cosmological constraints on dynamical dark energy model in $F(Q)$ gravity
• Conserved quantities in STEGR and applications
• Gravitational tensor and scalar modes in $f(Q,B)$ non-metric gravity
• Gravitational energy-momentum pseudo-tensor in Palatini and metric $f(R)$ gravity
• Gravitational radiation in higher order non-local gravity
• The energy-momentum complex in non-local gravity
• Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity
• Extended Geometric Trinity of Gravity
• Calculating the Hawking Temperature of Black Holes in $f(Q)$ Gravity Using the RVB Method: A Residue-Based Approach
• On the geometric origin of the energy-momentum tensor improvement terms
• The Noether formalism for constructing conserved quantities in teleparallel equivalents of general relativity

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