Quantum Inequalities for Quantum Black Holes.

We formulate spacetime inequalities applicable to quantum-corrected black holes to all orders of backreaction in semiclassical gravity. Namely, we propose refined versions of the quantum Penrose and reverse isoperimetric inequalities, valid for all known three-dimensional asymptotically anti-de Sitter quantum black holes. Previous proposals of the quantum Penrose inequality apply in higher dimensions but fail when applied in three dimensions beyond the perturbative regime.

Entropy Bounds for Rotating AdS Black Holes.

We propose novel thermodynamic inequalities that apply to stationary asymptotically anti-de Sitter (AdS) black holes. These inequalities incorporate the thermodynamic volume and refine the reverse isoperimetric inequality. To assess the validity of our conjectures, we apply them to a wide range of analytical black hole solutions, observing compelling evidence in their favor.

Higher-Dimensional Origin of Extended Black Hole Thermodynamics.

Holographic braneworlds are used to present a higher-dimensional origin of extended black hole thermodynamics. In this framework, classical, asymptotically anti-de Sitter black holes map to quantum black holes in one dimension less, with a conformal matter sector that backreacts on the brane geometry. Varying the brane tension alone leads to a dynamical cosmological constant on the brane, and, correspondingly, a variable pressure attributed to the brane black hole.