Classification theorem and properties of singular solutions to the Tolman-Oppenheimer-Volkoff equation

Understand

The Tolman-Oppenheimer-Volkoff (TOV) equation admits singular solutions in addition to regular ones.

• Here, we prove the following theorem.
• For any equation of state that (i) is obtained from an entropy function, (ii) has positive pressure and (iii) satisfies the dominant energy condition, the TOV equation can be integrated from a boundary inwards to the center.
• Hence, thermodynamic consistency of the EoS precludes pathological solutions, in which the integration terminates at finite radius (because of horizons, or divergences / zeroes of energy density).