General relativistic model for mixed fluid sphere with equation of state

Abstract

We generate a general frame work to solve the Einstein system with an equation of state that describe static spherically symmetric anisotropic matter distribution in terms of a generating function. It is examined for a Van der Waals type equation of state with a physically reasonable form of generating function. The model satisfies all the required major physical properties of a realistic star. It is shown to be stable in the low-density regime that may represent a liquid-gas mixed fluid sphere.

A comparative study of the linear and colour-flavour-locked equation of states for compact objects

“…The MIT Bag model motivated by work in QCD centred on quark confinement and asymptotic freedom [6] is essentially a linear EoS of the form p = (ρ − 4B)/3, where B is the Bag constant [7,8]. The MIT Bag model has been employed in several recent works to generate models of anisotropic spheres [9,10]. As pointed out by [11], this EoS cannot adequately account for the deconfinement of quarks at high density.…”

“…By appealing to the microphysics associated with strange matter, Rocha et al [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] adopt a CFL EoS of the form p r = αρ + βρ In this study we model spherically symmetric compact objects by adopting an isotropic line element which is simultaneously comoving. The interior matter configuration is described by an anisotropic fluid with unequal stresses in the radial and tangential directions.…”

Stability and improved physical characteristics of relativistic compact objects arising from the quadratic term in $$p_r = \alpha \rho ^2 + \beta \rho - \gamma $$

“…where the quantity Δ = p t − p r is a measure of the pressure anisotropy. A similar approach has been followed based on a linear equation of state [22]. The above system of equations governs the behaviour of the gravitational field for an imperfect fluid source.…”

Linear and Riccati equations in generating functions for stellar models in general relativity

“…The potential ν is found by a simple quadrature. Thus, Eq (28), which contains pr, y and a 1 , is the simplest generating function for any of them, when the other two are known. In some papers ansatze for y and pr were chosen [9], [10], [11], [12].…”

“…which follows from Eqs (26,28). Obviously, the resulting equation is not linear in y in general, but still may be solvable by choosing an ansatz for y.…”