The enriched phase structure of black branes in canonical ensemble

It is found that a necessary completion of phase structure of D-dimensional charged black p-brane ($p>0$) in a cavity requires two additional thermodynamical phases, the so-called “bubble of nothing” and/or the extremal brane, in canonical ensemble. This finding resolves the puzzle about the missing phases which are needed for the underlying phase diagram when $\tilde d = D - p - 3 \leq 2$ and gives a new (bubble) phase which can become globally stable when $\tilde{d}>2$. An analog of Hawking-Page transition is also found among other new phase transitions, giving a complete phase structure in this setup.