Spherical conformal models for compact stars

Abstract

We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass-radius limit and the surface red shift are consistent with observational constraints.

Static conformal models for anisotropic charged fluids

“…We regain the isotropic charged exact solutions of Usmani et al [33] and Mak and Harko [34]. The anisotropic distributions, where charge is absent, correspond to the results of Rahaman et al [35], Rahaman et al [36], Shee et al [14], Mafa Takisa et al [16], Esculpi and Aloma [37]. Models with both charge and anisotropy, include particular exact solutions of Esculpi and Aloma [37] and Newton Singh et al [15].…”

“…Newton Singh et al [15] discovered electrically charged dense stars in the presence of a static conformal Killing vector. Mafa Takisa et al [16], Kileba Matondo et al [17] and Kileba Matondo et al [18] generated new stellar models with conformal symmetries with radii, masses, densities and redshifts which are consistent with observed astronomical objects. These models have been found by integrating the Einstein-Maxwell field equations for selected forms of the metric functions.…”

A conformally flat realistic anisotropic model for a compact star

“…Some of them depend on the conformal factor and a matter component, which can be ρ [48], [49], or the mass m [50]. One can add here models with given λ [51], [52], since the expressions for ρ, m and λ are simply related. There is a model with a linear equation of state (LEOS) between p r and ρ [53], with two fluids [54] and another one with LEOS between the pressures [55].…”

Generalized anisotropic models for conformal symmetry

“…Manjonjo et al [10,11] showed that the two metric functions in static spherically symmetric spacetimes are related if a conformal Killing vector exists. Mafa Takisa et al [12] and Kileba Matondo et al [13,14] have shown that this relationship between the potentials may be exploited to model relativistic stars with anisotropy and electric charge. Therefore, the conformal symmetry approach is also useful in solving the nonlinear field equations for gravitating objects.…”

“…e.g. the stellar model in [12,13]. Recently, Ivanov [23] has proposed a conformally flat realistic anisotropic compact star model by using only analytical approach.…”