Anisotropic Spheres in General Relativity

Abstract

The possible importance of locally anisotropic equations of state for relativistic spheres is discussed by generalizing the equations of hydrostatic equilibrium to include these effects. The resulting change in maximum equilibrium mass M and surface redshift z is found analytically in the case of incompressibility (\rhoρ = const.) and a highly idealized expression for the anisotropy. Bondi’s analysis of isotropic spheres is generalized to include anisotropy, and the maximum surface redshift is investigated without reference to specific equations of state. A numerical model [with p(r) = \rho(r)/3p(r)=ρ(r)/3 and a special form of anisotropyl is then solved. In general, it is found that specific models lead to increases in zz typically of the same order of magnitude as the fractional anisotropy.