Hyperbolically symmetric sources in Palatini f(R) gravity

A thorough examination of static hyperbolically symmetric matter configuration in the context of Palatini f ( R ) gravitational theory has been carried out in this manuscript. Following the work of Herrera et al. (Phys. Rev. D 103 : 024037, 2021) we worked out the modified gravitational equations and matching conditions using the Palatini technique of variation in Einstein–Hilbert action. It is found from the evaluations that the energy density along with the contribution of dark source terms is inevitably negative which is quite useful in explaining several quantum field effects, because negative energies are closely linked with the quantum field theory. Such negative energies may also assist in time-travel to the past and formation of artificial wormholes. Furthermore, we evaluated the algebraic expressions for the mass of interior hyperbolical geometry and total energy budget, i.e., the Tolman mass of the considered source. Also, the structure scalars are evaluated to analyze the properties of matter configuration. Few analytical techniques are also presented by considering several cases to exhibit the exact analytical static solutions of the modified gravitational equations.