Week 26.02.2023 – 04.03.2023

The talk summarises recent work that illuminates our understanding of black hole entropy for supersymmetric black holes in Anti-de-Sitter space. We consider supersymmetric $AdS_3\times Y_7$ solutions of type IIB and $AdS_2\times Y_9$ solutions of $D=11$ supergravity. These can arise as the near horizon limit of black strings in $AdS_5$ and and black holes in $AdS_4$ spacetimes, respectively. We explain how novel extremisation techniques enable one to compute physical observables without explicitly solving Einstein equations. This allows one to identify infinite new classes of $AdS_3$/d=2 SCFT pairs, as well obtain a microstate counting interpretation for infinite classes of supersymmetric black holes in $AdS_4$. A sub-class of examples correspond to branes wrapping certain two-dimensional orbifolds known as spindles and this has opened up a new direction in AdS/CFT with novel connections to accelerating black holes.

Carroll geometries emerge as conformal boundaries of asymptotically flat spacetimes and have come to the forefront with the advent of flat holography. I will introduce these tools and show how they are used for unravelling the boundary manifestation of Ehlers' hidden Möbius symmetry present in four-dimensional Ricci-flat spacetimes that enjoy a time-like isometry. This is achieved in a designated gauge, where the three-dimensional Carrollian nature of the null conformal boundary is manifest and covariantly implemented. The action of the Möbius group is local on the space of Carrollian boundary data. Among these data, the Carrollian Cotton tensor plays a prominent role both in the Möbius electric/magnetic duality and for the determination of charges.

A key difference between black holes and ordinary thermal systems is the absence of a pressure-volume work term in the first law of black hole thermodynamics. It is possible to introduce such a work term for black holes in backgrounds with a cosmological constant by treating the cosmological constant as a pressure, offering a rich gravitational perspective on everyday phenomena. Missing, however, is justification for allowing variations of the cosmological constant. In this talk I will present a higher-dimensional origin of 'extended black hole thermodynamics' using holographic braneworlds. In this set-up, gravity is coupled to a lower-dimensional brane such that classical black holes in a bulk anti-de Sitter spacetime correspond to exact quantum corrected black holes localized on the brane, including all orders of semi-classical backreaction. Crucially, varying the tension of the brane leads to a dynamical cosmological constant on the brane, and, correspondingly, a variable pressure attributed to the brane black hole. In other words, standard thermodynamics of classical black holes induces extended thermodynamics of `quantum' black holes on a brane. As proof of concept, I will present the extended thermodynamics of the quantum BTZ black hole, also providing a microscopic interpretation using `double holography’.