On flat space limits of $AdS_4$ black holes

Abstract

With a view towards understanding flat space holography, we study the flat space limit of asymptotically $AdS_4$ black holes in gauged $\mathcal{N}=2$ supergravity. Using holographic renormalisation, we carefully analyse the flat space limit of the on-shell action of various black holes in this setting and make explicit the states that contribute to the partition function in this limit. We find several features: large black holes lead to a divergence in the partition function which can be understood as a thermodynamic volume divergence. Meanwhile, semiclassically, small black holes reproduce the partition function of their flat space counterparts, and we clarify the mapping between BPS, (near-)extremal or non-extremal black holes on both sides for charged and rotating solutions. Finally, by studying a suitable flat limit of the BPS Kerr-Newman-$AdS_4$ black hole in M-theory, we obtain a charged BPS solution in flat space. On the dual side, we determine a Carrollian-like limit on the known ABJM partition function on $S^1\times S^2$ at large $N$, and show that it reproduces the correct entropy of the BPS charged black hole in asymptotically flat space.