Solutions of the Oppenheimer--Volkoff Equations Inside 9/8$^{ths}$ of the Schwarzschild Radius

Abstract

We refine the Buchdahl 9/8 ths stability theorem for stars by describing quantitatively the behavior of solutions to the Oppenheimer–Volkoff equations when the star surface lies inside 9/8 ths of the Schwarzschild radius. For such solutions we prove that the density and pressure always have smooth profiles that decrease to zero as the radius r → 0, and this implies that the gravitational field becomes repulsive near r = 0 whenever the star surface lies within 9/8 ths of its Schwarzschild radius.