The general relativistic double polytrope for anisotropic matter

Abstract

A general formalism recently proposed to study Newtonian polytropes for anisotropic fluids is here extended to the relativistic regime. Thus, it is assumed that a polytropic equation of state is satisfied by, both, the radial and the tangential pressures of the fluid. Doing so the generalized Lane--Emden equations are obtained and solved. Some specific models are obtained, and their physical properties are discussed.