Thermal transitions of metastable M-branes

We use blackfold methods to analyse the properties of putative supergravity solutions in M-theory that describe the backreaction of polarised anti-M2 branes (namely, M₅ branes wrapping three-cycles with negative M2-brane charge) in the Cvetic-Gibbons-Lu-Pope background of eleven-dimensional supergravity. At zero temperature we recover the metastable state of Klebanov and Pufu directly in supergravity. At finite temperature we uncover a previously unknown pattern of mergers between fat or thin M₅-brane states with the thermalised version of the metastable state. At sufficiently small values of the anti-brane charge a single fat-metastable merger follows the same pattern recently discovered for polarised anti-D₃-branes in the Klebanov-Strassler solution in type IIB supergravity. We provide quantitative evidence that this merger is driven by properties of the horizon geometry. For larger values of the anti-brane charge the wrapped M₅-brane solutions exhibit different patterns of finite-temperature transitions that have no known counterpart in the anti-D₃ system in Klebanov-Strassler.