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.

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

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• The realistic models of relativistic stars in f(R) = R + alpha R^2 gravity
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• Wormholes in $R^2$-gravity within the $f(R,T)$ formalism
• Modified TOV in gravity's rainbow: properties of neutron stars and dynamical stability conditions
• Generating physically realizable stellar structures via embedding
• Stellar Structures in $f(\mathcal{G})$ Gravity with Tolman-Kuchowicz Spacetime
• Effects of Charge on Gravitational Decoupled Anisotropic Solutions in f(R) Gravity
• Dilatonic Equation of Hydrostatic Equilibrium and Neutron Star Structure
• Non-local $F(R)$-mimetic gravity
• Compact Objects by Gravitational Decoupling in f(R) Gravity
• Stellar Structures in $f(\mathcal{G})$ Gravity Admitting Noether Symmetries
• Neutron stars in Einstein-$\Lambda$ gravity: the cosmological constant effects
• Mimetic Compact Stars
• Noether symmetry in a nonlocal f(T) Gravity
• Stellar Structures admitting Noether Symmetries in $f(\mathcal{R},\mathcal{T})$ Gravity
• Properties of white dwarfs in Einstein-$\Lambda$ gravity
• Constraining Quadratic $f(R)$ Gravity from Astrophysical Observations of the Pulsar J0704+6620
• On the impact of non-local gravity on compact stars