Tolman-Oppenheimer-Volkoff equations in nonlocal f(R) gravity

Nonlocal f(R) gravity was proposed as a powerful alternative to general relativity (GR). This theory has potentially adverse implications for infrared (IR) regime as well as ultraviolet (UV) early epochs. However, there are a lot of powerful features, making it really user-friendly. A scalar-tensor frame comprising two auxiliary scalar fields is used to reduce complex action. However, this is not the case for the modification complex which plays a distinct role in modified theories for gravity. In this work, we study the dynamics of a static, spherically symmetric object. The interior region of space-time had rapidly filled the perfect fluid. However, it is possible to derive a physically based model which relates interior metric to nonlocal f(R). The Tolman-Oppenheimer-Volkoff (TOV) equations would be a set of first-order differential equations from which we can deduce all mathematical (physical) truths and derive all dynamical objects. This set of dynamical equations govern pressure p, density ρ, mass m and auxiliary fields {φ, ξ}. The full conditional solutions are evaluated and inverted numerically to obtain exact forms of the compact stars Her X-1, SAX J 1808.4-3658 and 4U 1820-30 for nonlocal Starobinsky model of f(→^-1 R) = →^-1 R+α(→^-1 R)². The program solves the differential equations numerically using adaptive Gaussian quadrature. An ascription of correctness is supposed to be an empirical equation of state P/P<inf>c</inf> = a (1-e^-b ρ/ρ<inf>c</inf>) for star which is informative in so far as it excludes an alternative nonlocal approach to compact star formation. This model is most suited for astrophysical observation.