Quasilocal Formalism and Black Ring Thermodynamics

TL;DR

Astefanesei and Radu apply a Brown-York quasilocal formalism with boundary counterterms to five-dimensional dipole black rings, showing that the dipole charge enters the first law analogously to a global charge and confirming the entropy/area relation via Gibbs-Duhem. They compute the mass and angular momentum from the boundary stress tensor, recover the expected thermodynamic structure, and analyze stability, finding neutral rings unstable to angular fluctuations. A complex quasi-Euclidean geometry is employed to define a consistent action and Gibbs potential, with further discussion of counterterm choices and possible holographic interpretations. The work provides a robust framework for thermodynamics of higher-dimensional black objects with nontrivial multipole structure.

Abstract

The thermodynamical properties of a dipole black ring are derived using the quasilocal formalism. We find that the dipole charge appears in the first law in the same manner as a global charge. Using the Gibbs-Duhem relation, we also provide a non-trivial check of the entropy/area relationship for the dipole ring. A preliminary study of the thermodynamic stability indicates that the neutral ring is unstable to angular fluctuations.