Stress-energy tensor for modified general relativity with quantum-deformed metric in Riemann spacetime
Year: 2026
Type: article
Abstract: The generalized noncommutative Heisenberg algebra, which is based on the generalized uncertainty principle, imposes a minimal length uncertainty on quantum mechanics (QM), on one hand. On the other hand, the quantum-induced space–time, which is based on quantum-deformed metric through geometric quantization, is proposed as additional curvatures on the relativistic tangent bundle on Finsler manifold. An additional terms that incorporates minimal length discretization along with second-order derivatives of tangent covectors, thereby suggesting an approach to reconcile the principles of QM with General Relativity (GR), is utilized for the construction of a torsion-free quantum-deformed metric on Riemann manifold. Consequently, it is proposed that quantum-induced revisions to the symmetric stress-energy tensor, source of space–time curvature, along with the current density related to the gauge transformations of gravity, ought to be taken into account in the matter Lagrangian with electromagnetic and scalar components. Vanishing covariant derivative of the quantum-induced stress-energy tensor suggests that the corresponding continuity equation implies that the gravitational fields do work on the classical and quantum matter and vice versa and the non-gravitational energy and momentum are no longer entirely conserved. For vanishing tangent covector derivatives and/or minimal length uncertainty, the classical formulations of the Einstein stress-energy tensor are retained and accordingly that of GR and QM. We conclude that the proposed quantum-induced formulation of the stress-energy tensor is fundamentally suitable for both classical and quantum-induced field equations.
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162094739
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