Dynamical Black Holes: Apparent Horizon Versus Energy Conditions

Dynamical black holes have an apparent horizon as one of their characteristics. The later might be null, time-like, or space-like surfaces that define the evolution of a black hole. Our study examines how an apparent horizon's behavior is influenced by the null energy condition in spherically-symmetric spacetime. If the location of an apparent horizon and the NEC horizon coincide, it is proven to be null surface. The outer apparent horizon may appear time-like despite the growth of the black hole mass, which must be astrophysical important because the shadow of a black hole always decreases. We show that if NEC is satisfied everywhere in spacetime, then the dynamical black hole asymptotically tends to Vaidya black hole. Our research demonstrates that evaporation of a regular black hole consistently results in a horizonless object with a regular center, which opens the possibility of elucidating the information loss paradox.