Role of pressure anisotropy on relativistic compact stars

We investigate a compact spherically symmetric relativistic body with anisotropic particle pressure profiles. The distribution possesses characteristics relevant to modeling compact stars within the framework of general relativity. For this purpose, we consider a spatial metric potential of Korkina and Orlyanskii [Ukr. Phys. J. 36, 885 (1991)] type in order to solve the Einstein field equations. An additional prescription we make is that the pressure anisotropy parameter takes the functional form proposed by Lake [Phys. Rev. D 67, 104015 (2003)]. Specifying these two geometric quantities allows for further analysis to be carried out in determining unknown constants and obtaining a limit of the mass-radius diagram, which adequately describes compact strange star candidates like Her X-1 and SMC X-1. Using the anisotropic Tolman-Oppenheimer-Volkoff equations, we explore the hydrostatic equilibrium and the stability of such compact objects. Then, we investigate other physical features of this model, such as the energy conditions, speeds of sound, and compactness of the star, in detail and show that our results satisfy all the required elementary conditions for a physically acceptable stellar model. The results obtained are useful in analyzing the stability of other anisotropic compact objects like white dwarfs, neutron stars, and gravastars.

Figure 1

Variation for energy density and radial and transverse pressures have been plotted against the radial parameter, while the metric potentials and anisotropic function [Eq. (10)] have been displayed in the second row for the compact star Her X-1 and SMC X-1. The parameter values which we have used are given in Table 1.

Figure 2

The energy conditions, namely the null energy condition (NEC), weak energy condition (WEC), and strong energy condition (SEC), are shown here for the compact stars SMC X-1 and Her X-1. The numerical values of the constants are given in Table 1.

Figure 3

We have plotted different forces, namely the gravitational force ($F_g$), hydrostatic force ($F_h$), and anisotropic force ($F_a$), for studying the effect of the anisotropy on the stability of compact stars. See Subsection C for details about the stable configuration mode.

Figure 4

A plot of the characteristics for sound propagation $v_s^2=dp/d\rho$ along the radial and transverse direction for the same stellar model. We have shown that the speed of sound is less than unity within the stellar radii by making a choice similar to that in Fig. 1.