In the previous work we introduced a new static cylindrically symmetric vacuum solutions in Weyl coordinates in the context of the metric f(R) theories of gravity [1]. Now we obtain a 2parameter family of exact solutions which contains cosmological constant and a new parameter as β. This solution corresponds to a constant Ricci scalar. We proved that in f (R) gravity , the constant curvature solution in cylindrically symmetric cases is only one member of the most generalized Tian family in GR. We show that our constant curvature exact solution is applicable to the exterior of a string. Sensibility of stability under initial conditions is discussed.
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 ρ, mass m and auxiliary fields {ψ, 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 non-local StarobinskyThe program solves the differential equations numerically using adaptive Gaussian quadrature. An ascription of correctness is supposed to be an empirical equation of state P Pc = a(1 − e −b ρ ρc ) for star which is informative in so far as it excludes an alternative non local approach to compact star formation. This April 7, 2015 0:52 WSPC/INSTRUCTION FILE TOV-NONLOCAL-IJMPA 2 D. MOMENI et al. model is most suited for astrophysical observation.
We calculate the thermodynamic properties of strange quark matter by using the density and temperature dependent particle mass model of Wen et al. For the interaction Hamiltonian we use the one gluon exchange interaction obtained from the Fermi liquid picture. We let the QCD coupling (αc) be constant or vary with density and temperature. A new set of mass scalings for quarks is evaluated from the present interaction, which can be used with thermodynamic formulas derived by Wen et al. Similar to β-stable matter, no stability is found in strange quark matter. Finally, it is shown that the present equation of state of strange quark matter becomes harder with respect to that obtained using the string model, specially with non-constant QCD coupling.
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