A new model for charged anisotropic compact star

Abstract

In this article we obtain a new anisotropic solution for Einstein's field equation of embedding class one metric. The solution is representing the realistic objects such as Her X − 1 and RXJ 1856 − 37. We perform detailed investigation of both objects by solving numerically the Einstein field equations under with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if anisotropy is zero everywhere inside the star then the density and pressures will become zero and metric turns out to be flat. We report our results and compare with the above mentioned two compact objects on a number of key aspects: the central density, the surface density onset and the critical scaling behavior, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in relativistic compact star.

A family of charged compact objects with anisotropic pressure

“…Work on rotating stars utilise an axis-symmetric metric to describe the stellar interior [11,12]. Recently there has been a surge in obtaining exact solutions of the Einstein field equations via embedding [13][14][15][16][17][18][19][20][21]. In 1947 Karmarkar obtained a restriction which is a necessary condition for embedding a spherically symmetric spacetime in four dimensions into a flat five-dimensional spacetime.…”

Generating physically realizable stellar structures via embedding

“…Karmarkar derived the necessary condition for a general spherically symmetric metric to be of class one [21]. In general, if the lowest number of dimensions of flat space in which a Riemannian space of dimension n can be embedded in n + p, then the Riemannian space is referred to as class p. Class one space-times have been successfully utilised to model compact objects such as strange star candidates, neutron stars and pulsars [22][23][24][25][26][27][28]. These theoretical models accurately predict and agree with observations regarding the masses, radii, compactness and densities of these objects within experimental error.…”

Solution of the Einstein–Maxwell equations with anisotropic negative pressure as a potential model of a dark energy star

“…(27) and a > 2k 3 we get the bound on the charge-radius ratio as Stability of an ordinary star depends on the behavior of radial sound velocity V 2 r = dpr dρ and transverse sound velocity V 2 t = dpt dρ . The region in which, the radial sound velocity is greater than the transverse sound velocity is called stable region [31,32]. As in Section 2 it is mentioned that the dark energy stars with equation of state p r = −ρ do not satisfy the causality condition, however, we can check the stability region.…”