Tolman-Oppenheimer-Volkoff equations in non-local $f(R)$ gravity

Abstract

Non-local $f(R)$ gravity was proposed as a powerfull alternative to general relativity (GR) . This theory has potentially adverse implications for infrared (IR) regime as well as ultraviolent(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, 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 spacetime had rapidly filled the perfect fluid. However, it is possible to derive a physically based model which relates interior metric to non-local $f(R)$. 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 $\rho$, mass $m$ and auxiliary fields $\{\psi ,\xi \}$. 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 non-local Starobinsky model of $f({\square }^{-1}R)={\square }^{-1}R+\alpha ({\square }^{-1}R{)}^2$. The program solves the differential equations numerically using adaptive Gaussian quadrature. An ascription of correctness is supposed to be an empirical equation of state $\frac{P}{P_c}=a(1-e^{-b\frac{\rho }{{\rho }_c}})$ for star which is informative in so far as it excludes an alternative non local approach to compact star formation. This model is most suited for astrophysical observation.

Accepted in "International Journal of Modern Physics A",20 pages, 10 figures, 2 tables

References in corpus (21)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark energy in modified Gauss-Bonnet gravity: late-time acceleration and the hierarchy problem
• Dark energy cosmology from higher-order, string-inspired gravity and its reconstruction
• Future of the universe in modified gravitational theories: Approaching to the finite-time future singularity
• Extreme neutron stars from Extended Theories of Gravity
• Modified non-local-F(R) gravity as the key for the inflation and dark energy
• Generalized energy conditions in Extended Theories of Gravity
• Nonperturbative models of quark stars in $f(R)$ gravity
• Accelerating cosmologies from non-local higher-derivative gravity
• Phantom and non-phantom dark energy: The cosmological relevance of non-locally corrected gravity
• Wormholes in a viable f(T) gravity
• Anisotropic Compact Stars in $f(G)$ Gravity
• Reconstructing the Distortion Function for Nonlocal Cosmology
• Attractor Solutions in f(T) Cosmology
• Noether Symmetry Approach in Gauss-Bonnet Cosmology
• Energy conditions and current acceleration of the universe
• Cylindrical Solutions in Modified f(T) Gravity
• One-loop effective action for non-local modified Gauss-Bonnet gravity in de Sitter space
• Tolman-Oppenheimer-Volkoff Equations in Modified Gauss-Bonnet Gravity
• Modified gravity: walk through accelerating cosmology
• The Weak Field Limit of Fourth Order Gravity

Cited by in corpus (2)

• Wormholes in $R^2$-gravity within the $f(R,T)$ formalism
• Effects of Charge on Gravitational Decoupled Anisotropic Solutions in f(R) Gravity