Constraining the number of horizons with energy conditions

Understand

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.