Name for a state of an automaton that can't be left

Question

In an automaton, we might have a state that once reached cannot be left.

It is for example for Ø in

Is there a common/official name for such a state ?

Answer 1

In the notes we use at my institution, it's called a black hole.

Answer 2

Such a state is usually called a sink state or sometimes a dead state or a zero state. "Sink state" seems to be the most largely accepted terminology in the literature.

Answer 3

From Theory and Applications of Models of Computation. 9th Annual Conference:

A sink state in an S-automaton is a state whose all outgoing transitions loop into the state itself.