On the Robustness of Holographic Dualities: AdS Black Holes and Quotient Spaces

This dissertation is a collection of works on different topics based on holographic dualities. The dualities studied here are the Kerr/CFT and AdS/CFT correspondence and the researches carried on aim to check their robustness for some particular theories of gravity. We first demonstrate that the Kerr/CFT duality can be extended to superentropic black holes, which have non-compact horizons with finite area. The duality is robust as the near horizon limit of these black holes commutes with their ultraspinning limit. We notice that the duality holds as well for both the singly-spinning superentropic black holes in four dimensions and the double-spinning superentropic black holes of gauged supergravity in five dimensions. Second, we test the AdS/CFT duality in Lovelock gravity theories or higher curvature theories of gravity in which we investigate the holographic Smarr relation beyond the large N limit. By making use of the holographic dictionary, we obtain a holographic equation of state in the conformal field theories (CFTs) dual to AdS spacetimes. We check the validity of this equation of state for a variety of non-trivial black holes including rotating planar black holes in Gauss-Bonnet-Born-Infeld gravity and non-extremal rotating black holes in minimal 5d gauged supergravity. In the remaining part of this dissertation we return to investigate AdS/CFT duality, but now focus on computational complexities defined in the CFTs dual to AdS black holes. The first one is the volume-complexity, which consists in a duality between a quantum information metric or Bures metric in a (d+1)-dimension CFT and the volume of a maximum time slice in the dual (d+2)-dimension AdS spacetime. We examine specific cases of black holes such as the Banados-Teitelboim-Zanelli (BTZ) and the planar Schwarzschild-AdS black holes in (d+2)-dimensions, along with their geon counterparts. Geons being quotient spaces of AdS black holes obtained from the identification of the left and right boundaries of their conformal diagrams. We find that the proposed duality relation remains the same for the geon space with a topological factor of 4. The second one is the action-complexity, which conjectures a duality between the action of an AdS bulk evaluated on a Wheeler-De Witt (WDW) patch and a CFT computational complexity providing a measure of the minimum number of gates necessary to reach a target state from a reference state. We compute the dependence of the CFT complexity on a boundary temporal parameter (time) and find that its variation with time is commensurate with the rate of change of the bulk action on the WDW patch. We remark that the action-complexity duality holds for the geons associated to these black holes (with a topological factor up to 4) as well