Constraining the number of horizons with energy conditions.

We show that the number of horizons of static black holes are constrained a lot by classic matter satisfied some energy conditions. With very general assumptions, we prove that if the interior of a black hole is dominated by classical matter, there is at most one non-degenerated inner horizon behind the event horizon; in addition, if the event horizon is degenerated, there exists no inner horizon. Our result offers some universal restrictions on the number of horizons. Interestingly and importantly, it also suggests that classical matter not only promotes the formation of event horizon but also prevents the appearance of multiple horizons inside black holes. Furthermore, using the geometrical construction, we obtain a radially conserved quantity which is valid for general static spacetimes.