Equation of state for anisotropic spheres

Abstract

We present a new class of exact interior solutions for anisotropic spheres to the Einstein field equations with a prescribed energy density. This category of solutions has similar energy density profiles to the models of Chaisi and Maharaj (Gen. Rel. Grav. 37, 1177-1189) whose approach we follow in the integration process. A distinguishing feature of the solutions presented is that they satisfy a barotropic equation of state linearly relating the radial pressure to the energy density. Keywords Anisotropic relativistic stars · Exact solutions · Compact spheresSince the pioneering work of Bowers and Liang [1] on anisotropic stars many researchers, in recent years, have studied anisotropic matter in the context of general relativity; these include the investigations of Dev and Gleiser [2,3], Mak and Harko [4,5] and Herrera et al. [6,7] in different relativistic astrophysical situations. This research has been motivated on the grounds that anisotropy affects the critical mass, surface redshift and stability of highly compact relativistic bodies. Anisotropic matter appears to be a vital ingredient in the modelling of boson stars and strange matter with densities higher than neutron stars as pointed out by Mak and Harko [4] and Sharma and Mukherjee [8]

A class of relativistic stars with a linear equation of state

“…Secondly, we choose an EOS which linearly relates the radial pressure to the energy density. Maharaj & Chaisi (2006) have demonstrated that this simple EOS is consistent in the modelling of compact matter such as neutron stars and quasi‐stellar objects. The EOS yields values of surface redshifts and masses that correspond to realistic stellar objects such as Her X‐1 and Vela X‐1 (Gokhroo & Mehra 1994; Chaisi & Maharaj 2005).…”

“…Our analysis depends critically on the choice of the mass function given by so that a linear EOS is possible. Note that some other treatments, such as the result of Maharaj & Chaisi (2006), with a linear EOS has the unrealistic feature of vanishing energy density at the boundary. Our model does not suffer from this defect.…”

A conformally flat realistic anisotropic model for a compact star

“…which is very simple. In more general form it was used in the past, [56], [70], [71], [72], [73], [74], [75], [76], [77], [78], [79], [80], [81]. In the context of conformal flatness it was used in [40], Example 4, and [42], model III but only a partial physical analysis has been done.…”

Charged anisotropic compact star core-envelope model with polytropic core and linear envelope

“…Linear EoS is consistent in the modeling of compact objects, one can achieve modeling of anisotropic spherical objects with quark matter distributions [74,75]. It is suitable in retrieving the mass-radius relationship and values of surface redshifts corresponding to realistic stars [76,77]. For envelope region, we assume the same anisotropic Tolman VII [61] with linear EoS…”