Analysis of the cosmological Oppenheimer-Volkoff equations

We formulate the Oppenheimer-Volkoff equations with nonzero cosmological co nstant, Lambda. We analyze the behavior of solutions (under mild assumption s on the equation of state). We prove that solutions of the cosmological Op penheimer-Volkoff equations are either singularity-free or else M(r)< 0 for some r > 0. [Here M(r) represents the total mass inside radius r.] We show that this behavior is independent of the magnitude of Lambda when Lambda l ess than or equal to 0. In the case where Lambda > 0, we show that these co nclusions hold provided that the solution is contained within a ball of rad ius 1/root Lambda. We prove that if M(r)< 0 for some r > 0 then the pressur e tends to infinity before r=0. (C) 2000 American Institute of Physics. [S0 022-2488(00)05605-X].