No Inner-Horizon Theorem for Black Holes with Charged Scalar Hairs

Understand

We establish a no inner-horizon theorem for black holes with charged scalar hairs.

• Considering a general gravitational theory with a charged scalar field, we prove that there exists no inner Cauchy horizon for both spherical and planar black holes with non-trivial scalar hair.
• The hairy black holes approach to a spacelike singularity at late interior time.
• This result is independent of the form of scalar potentials as well as the asymptotic boundary of spacetimes.