Some Properties of an Oscillating Fluid Sphere in General Relativity

Abstract

Nariai's singularity-free model for a relativistic, oscillating fluid sphere is investigated. It is shown that both density and pressure have negative gradients. Hernandez/Misner's criterium for a trapped surface to exist is not fulfilled, so the surface of the sphere is outside the Schwarzschild surface. The inequalities ρ - p > 0 and ρ - 3p > 0 will not hold for arbitrary choice of the three parameters e, S1, S2 which specify the degree of non-homogeneity, minimum and maximum size of the pulsating object respectively, If the degree of non-homogeneity is small, however, both the inequalities above are fulfilled. The velocity of the matter has positive gradient and is smaller than the velocity of light throughout the sphere.