  The AdS/CFT correspondence may give a new way of understanding field theories
in extreme conditions, as in the quark-gluon plasma phase of quark matter. The
correspondence normally involves asymptotically AdS black holes with dual field
theories which are defined on locally flat boundary spacetimes; the implicit
assumption is that the distortions of spacetime which occur under extreme
conditions do not affect the field theory in any unexpected way. However, AdS
black holes are [to varying degrees] "fragile", in the sense that they become
unstable to stringy effects when their event horizons are sufficiently
distorted. This implies that field theories on curved backgrounds may likewise
be unstable in a suitable sense. We investigate this phenomenon, focussing on
the "fragility" of AdS black holes with flat event horizons. We find that, when
they are distorted, these black holes are always unstable in string theory.
This may have consequences for the detailed structure of the quark matter phase
diagram at extreme values of the spacetime curvature.
