Anisotropic generalization of Buchdahl bound for specific stellar models

Anisotropy is one factor that appears to be significantly important in the studies of relativistic compact stars. In this paper, we make a generalization of the Buchdahl limit by incorporating an anisotropic effect for a selected class of exact solutions describing anisotropic stellar objects. In the isotropic case of a homogeneous distribution, we regain the Buchdahl limit 2M/R <= 8/9. Our investigation shows a direct link between the maximum allowed compactness and pressure anisotropy vi-a-vis geometry of the associated 3-space.

Automated summary

The study reveals a direct link between the maximum allowed compactness and pressure anisotropy in the context of describing anisotropic stellar objects, as well as the geometry of the associated 3-space.