A conformally flat realistic anisotropic model for a compact star

Abstract

A physically realistic stellar model with a simple expression for the energy density and conformally flat interior is found. The relations between the different conditions are used without graphic proofs. It may represent a real pulsar.

General relativistic model for mixed fluid sphere with equation of state

“…where y is given by (25). The solution (26)-(31) is given in simple elementary function so it may be used to model an anisotropic star with Van der Waals equation of state.…”

“…Many exact solutions to the field equations have been generated by different approaches with generalized forms for one of the gravitational potentials that does have an equation of state (EoS) (linear [2][3][4][5][6][7], quadratic [8][9][10], polytropic [11][12][13][14][15][16], Van der Waals [17], etc.) and without [18][19][20][21][22][23][24][25] a particular barotropic EoS relating the pressure to the energy density. However, among large number of such work reported over the years, relatively few of these solutions correspond to non-singular metric functions with physically acceptable energy momentum tensor.…”

Generalized anisotropic models for conformal symmetry

“…As a significance of the following algorithm, the generating functions of anisotropic fluid distribution for conformal symmetry as follows (using the Eqs. (19) and (23)):…”

“…the stellar model in [12,13]. Recently, Ivanov [23] has proposed a conformally flat realistic anisotropic compact star model by using only analytical approach. The study of Herrera and Di Prisco [22] is related to the important physically geometry system of static axial symmetry.…”

Are there any models with homogeneous energy density?

“…Secondly, it is shown there are no spherically symmetric dynamic solution consistent with homogeneous energy density and, for this case the shear-free assumption is equivalent to the isotropic pressure condition. Finally, a circular equivalence is shown among the most frequent conditions considered for the spherical symmetric case: homogeneous density, isotropy in pressures, conformally flatness [22][23][24][25][26][27][28][29][30][31][32][33][34][35] and shear-free conditions [36][37][38][39][40][41][42][43][44]. It is shown that due to the regularity conditions at the center of the matter distribution, the imposition of any two of them necessarily leads to the static case.…”