Buchdahl surface of anisotropic compact objects

Abstract

The equations of structure for anisotropic stars can be recast into a three-dimensional regular and autonomous dynamical system in a compact state space. When these equations are studied from a dynamical systems viewpoint, they allow us to obtain robust insights into the nature of the Buchdahl limit for anisotropic compact objects that are valid for a large class of equations of state. Here, using the Bowers-Liang ansatz for the anisotropy term, we show that anisotropic stars are able to exceed the standard (i.e. isotropic) Buchdahl bound, and determine a necessary condition on the equation of state that allows for this violation.