Dynamics of charged hyperbolically symmetric matter in modified gravity

Abstract

We have conducted an in-depth investigation of static anisotropic matter configurations surrounded by electromagnetic field and possessing hyperbolically symmetric geometry by examining their physical characteristics in the framework of Palatini version of f(R) gravitational theory. Choosing the comoving coordinates, we define a canonical orthonormal tetrad and obtain the components of stress-energy tensor in locally Minkowskian frame. Working out the Palatini–Maxwell equations and the interior mass function for such a symmetry, it comes out that the energy density appears as a negative quantity which results in the development of a vacuole in the vicinity of the central region of the symmetry depicting that this region cannot be occupied by matter. We have also assessed the hydrostatic equilibrium equation and the source of tidal forces for the symmetry (i.e. Weyl scalar) and the active gravitational mass. Few scalar functions are then obtained out of the orthogonal decomposition of the Riemann curvature tensor and are utilized for the comprehension of physical characteristics of the matter configuration. Certain explicit solutions to the Palatini–Maxwell equations are also rendered with the help of two physical variables acting as generating functions.