Bounds on the basic physical parameters for anisotropic compact general relativistic objects

TL;DR

This paper establishes theoretical bounds on key physical parameters of anisotropic compact stars within general relativity, considering the effects of a cosmological constant and anisotropy.

Contribution

It provides new upper and lower limits for mass-radius ratio, anisotropy, redshift, and energy for anisotropic stars, including the impact of the cosmological constant.

Findings

Anisotropic stars can be more compact than isotropic ones.

Surface redshift greater than two may indicate anisotropy.

Existence of a minimum mass configuration with given anisotropy.

Abstract

We derive upper and lower limits for the basic physical parameters (mass-radius ratio, anisotropy, redshift and total energy) for arbitrary anisotropic general relativistic matter distributions in the presence of a cosmological constant. The values of these quantities are strongly dependent on the value of the anisotropy parameter (the difference between the tangential and radial pressure) at the surface of the star. In the presence of the cosmological constant, a minimum mass configuration with given anisotropy does exist. Anisotropic compact stellar type objects can be much more compact than the isotropic ones, and their radii may be close to their corresponding Schwarzschild radii. Upper bounds for the anisotropy parameter are also obtained from the analysis of the curvature invariants. General restrictions for the redshift and the total energy (including the gravitational contribution) for anisotropic stars are obtained in terms of the anisotropy parameter. Values of the surface redshift parameter greater than two could be the main observational signature for anisotropic stellar type objects.