Constraining the number of horizons with energy conditions

Abstract

We show that the number of horizons of static black holes can be strongly constrained by energy conditions of matter fields. After a careful clarification on the ‘interior’ of a black hole, we prove that if the interior of a static black hole satisfies strong energy condition or null energy condition, there is at most one non-degenerated inner Killing horizon behind the non-degenerated event horizon. Our result offers some universal restrictions on the number of horizons. Interestingly and importantly, it also suggests that 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.