Finite-cutoff holography and quasilocal thermodynamics of BTZ black holes in a cavity

Abstract

We develop a finite-cutoff formulation of BTZ black-hole thermodynamics in which a circular cavity at radius $R$ is treated as a genuine holographic screen. The resulting ensemble is simultaneously a quasilocal gravitational system in the Brown--York sense and a finite-radius realization of holography in AdS$_3$. This viewpoint organizes the thermodynamics of static and rotating BTZ geometries in terms of local intensive data measured at the wall, the corresponding quasilocal stress tensor, and the radial Hamilton--Jacobi flow of the on-shell action. We show how the cavity description naturally connects to finite-cutoff AdS/CFT and to the thermodynamics of $T\bar T$-deformed two-dimensional theories. The program developed in this paper includes a grand-canonical treatment of rotating BTZ black holes, an off-shell free-energy landscape for the cavity ensemble, a finite-size Hawking--Page transition with a holographic interpretation, radial flow equations for energy and pressure, and a microscopic density-of-states analysis adapted to finite cutoff. The cavity radius therefore plays a dual role: it is a thermodynamic control parameter in the bulk and an RG scale in the dual description.