New exact solutions in a model of f(R) gravity and their physical properties

ABSTRACT: Some new exact solutions in a model of f (R) gravity are obtained. Three kinds of matter fields have been used to obtain exact analytic solutions. In the first solution, the Yang-Mills fields are incorporated as a matter field at constant curvature condition. In the second and third solutions, the linear and nonlinear electromagnetic fields are used as matter fields. Thermodynamic properties are explored for those solutions that admit black holes. The occurrence of naked singularities in the solutions sourced by linear electromagnetic fields is investigated within the context of quantum mechanics. The waves obeying the massless Klein-Gordon, Maxwell and Dirac fields are used to probe the singularity. It is shown that the classical curvature singularity remains singular even if it is probed with quantum waves rather than classical particles. Keywords: Black hole solution, f(R) Gravity, Yang-Mills, Linear and Nonlinear Electromagnetism, Quantum singularities.