Dynamical black holes: Apparent horizon versus energy conditions

One of the characteristics of a dynamical black hole is the apparent horizon. Initially it was assumed that this surface is spacelike. However, further studies have shown that it can be both and null and timelike. Recent studies of the black hole shadow have demonstrated the connection between energy conditions and the black hole shadow [6] . In this paper, we establish a connection between the behavior of the apparent horizon and energy conditions. We prove that the evaporation of regular black holes always leads to the formation of a horizonless object. We introduce notions of NEC horizon and prove that the apparent horizon can be null surface if and only if it coincides with the NEC horizon. We also prove that energy conditions can lead to a situation when the mass of the black hole grows and the apparent horizon decreases, which can open the way to the explanation of the information loss paradox.