Interior marginally outer trapped surfaces in Hayward black holes

Abstract

We locate interior marginally outer trapped and marginally outer trapped open surfaces (MOTS/MOTOS) in the regular Haward metric with parameter $b$ for which a critical (extremal) value $b=b_c$ demarcates when the spacetime admits no horizon and when it admits inner and outer horizons. We identify self-intersecting MOTS which occur in pairs. For $b$ close to the critical value, there are no self-intersecting MOTS/MOTOS, and one can fine-tune $b$ so that the interior contains only near-spherical MOTS. We also show that in a neighborhood of the inner horizon for certain values of $b$, upon reduction of the problem to a singular Sturm-Liouville problem, the locations of the MOTS are given by hypergeometric functions, the eigenspace of the operator for which is complete, not discrete, and discontinuous.