  We analyze the quantum process in which a cosmic string breaks in an anti-de
Sitter (AdS) background, and a pair of charged or neutral black holes is
produced at the ends of the strings. The energy to materialize and accelerate
the pair comes from the strings tension. In an AdS background this is the only
study done in the process of production of a pair of correlated black holes
with spherical topology. The acceleration $A$ of the produced black holes is
necessarily greater than (|L|/3)^(1/2), where L<0 is the cosmological constant.
Only in this case the virtual pair of black holes can overcome the attractive
background AdS potential well and become real. The instantons that describe
this process are constructed through the analytical continuation of the AdS
C-metric. Then, we explicitly compute the pair creation rate of the process,
and we verify that (as occurs with pair creation in other backgrounds) the pair
production of nonextreme black holes is enhanced relative to the pair creation
of extreme black holes by a factor of exp(Area/4), where Area is the black hole
horizon area. We also conclude that the general behavior of the pair creation
rate with the mass and acceleration of the black holes is similar in the AdS,
flat and de Sitter cases, and our AdS results reduce to the ones of the flat
case when L=0.
