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.