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Role of modified scalar variables in the modeling of spherical fluids. (English) Zbl 1393.83019

Summary: The aim of this work is to analyze the role of shear evolution equation in the modeling of relativistic spheres in \(f(R)\) gravity. We assume that non-static diagonally symmetric geometry is coupled with dissipative anisotropic viscous fluid distributions in the presence of \(f(R)\) dark source terms. A specific distribution of \(f(R)\) cosmic model has been assumed and the spherical mass function through generic formula introduced by Misner-Sharp has been formulated. Some very important relations regarding Weyl scalar, matter variables and mass functions are being computed. After decomposing orthogonally the Riemann tensor, some scalar variables in the presence of \(f(R)\) extra degrees of freedom are calculated. The effects of the polynomial modified structure scalars in the modeling through Weyl, shear, expansion scalar differential equations are investigated. The energy density irregularity factor has been calculated for both anisotropic radiating viscous with varying Ricci scalar and for dust cloud with present Ricci scalar corrections.

MSC:

83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
83C22 Einstein-Maxwell equations
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
70F15 Celestial mechanics
70H40 Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics
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