In this article, we investigate the geometric and physical properties of relativistic magnetofluid spacetimes endowed with the $ Q $-curvature tensor within the framework of $ f(R, T, R_{ij}T^{ij}) $-gravity by analyzing the resulting differential equations and their constraints. We derive the explicit form of the magnetofluid energy-momentum tensor and establish the corresponding modified field equations. We demonstrate that a $ Q $-flat magnetofluid spacetime satisfying the field equations of $ f(R, T, R_{ij}T^{ij}) $-gravity leads to significant constraints on the equation of state, restricting the admissible solutions to vacuum or de Sitter-type configurations. Furthermore, we analyze the energy conditions for this setup and show that the strong energy condition (SEC) is violated, which is a standard indicator of accelerated expansion and is consistent with the current observational evidence for the late-time acceleration of the universe. We also examine the case of a divergence-free $ Q $-curvature tensor and establish connections with Codazzi-type Ricci tensors and Yang pure spaces. To demonstrate the applicability of our results, we consider four specific models: Starobinsky-type, matter-coupling, nonminimal coupling, and combined models. For each model, we derive the effective energy density and pressure and analyze the energy conditions graphically using Mathematica. For the chosen parameter ranges, SEC violation is observed across all considered models of $ Q $-flat magnetofluid spacetimes in $ f(R, T, R_{ij}T^{ij}) $-gravity.
Citation: Lalnunenga Colney, Mohammad Nazrul Islam Khan. Q-curvature tensor and energy conditions in magnetofluid spacetimes under $ f(R, T, R_{ij}T^{ij}) $-gravity[J]. AIMS Mathematics, 2026, 11(9): 31963-31989. doi: 10.3934/math.20261257
In this article, we investigate the geometric and physical properties of relativistic magnetofluid spacetimes endowed with the $ Q $-curvature tensor within the framework of $ f(R, T, R_{ij}T^{ij}) $-gravity by analyzing the resulting differential equations and their constraints. We derive the explicit form of the magnetofluid energy-momentum tensor and establish the corresponding modified field equations. We demonstrate that a $ Q $-flat magnetofluid spacetime satisfying the field equations of $ f(R, T, R_{ij}T^{ij}) $-gravity leads to significant constraints on the equation of state, restricting the admissible solutions to vacuum or de Sitter-type configurations. Furthermore, we analyze the energy conditions for this setup and show that the strong energy condition (SEC) is violated, which is a standard indicator of accelerated expansion and is consistent with the current observational evidence for the late-time acceleration of the universe. We also examine the case of a divergence-free $ Q $-curvature tensor and establish connections with Codazzi-type Ricci tensors and Yang pure spaces. To demonstrate the applicability of our results, we consider four specific models: Starobinsky-type, matter-coupling, nonminimal coupling, and combined models. For each model, we derive the effective energy density and pressure and analyze the energy conditions graphically using Mathematica. For the chosen parameter ranges, SEC violation is observed across all considered models of $ Q $-flat magnetofluid spacetimes in $ f(R, T, R_{ij}T^{ij}) $-gravity.
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Lalnunenga Colney, Mohammad Nazrul Islam Khan. Q-curvature tensor and energy conditions in magnetofluid spacetimes under $ f(R, T, R_{ij}T^{ij}) $-gravity[J]. AIMS Mathematics, 2026, 11(9): 31963-31989. doi: 10.3934/math.20261257
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