  We set forth a new type of phase transition that might take place in
gravitational theories whenever higher-curvature corrections are considered. It
can be regarded as a sophisticated version of the Hawking-Page transition,
mediated by the nucleation of a bubble in anti-de Sitter (AdS) space. The
bubble hosts a black hole in its interior, and separates two spacetime regions
with different effective cosmological constants. We compute the free energy of
this configuration and compare it with that of thermal AdS. The result suggests
that a phase transition actually occurs above certain critical temperature,
ultimately changing the value of the cosmological constant. We discuss the
consistency of the thermodynamic picture and its possible relevance in the
context of AdS/CFT.
