Complexity and Dynamics of Radiating Hyperbolically Self-Gravitating Systems

In this work, we explore the evolution of non-static, radiating, shearing, and hyperbolically symmetric stellar configurations within the framework of general relativity by imposing the Euclidean condition. To model the interior spacetime, we consider a non-static hyperbolically symmetric fluid distribution undergoing gravitational collapse in the presence of anisotropic stresses and heat dissipation. We derive the corresponding gravitational field equations for the anisotropic matter content. We use the Euclidean condition, which simplifies the equations of motion by establishing a direct relationship between the metric functions and allows the construction of exact analytic stellar models. By smoothly matching the interior spacetime to the hyperbolic Vaidya geometry across the boundary hypersurface, the appropriate boundary conditions are obtained. Explicit expressions for the physical variables are derived, including the energy density, radial and tangential pressures, heat flux, anisotropic factor, and hyperbolic mass function. The effects of density inhomogeneity, dissipative heat flux, and pressure anisotropies on the dynamical evolution of hyperbolic stellar matter are analyzed in detail. The presented analytical solution may provide a useful application of the complexity factor in the dynamics of non-static hyperbolically symmetric matter distributions.

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