Higher spin black hole entropy in three dimensions

TL;DR

This paper derives a general entropy formula for three-dimensional black holes with spin-3 fields, linking it to horizon area and spin-3 charge, and confirms it reduces to known results in specific limits.

Contribution

It introduces a new, general entropy formula for 3D black holes with spin-3 fields, based on horizon geometry and thermodynamic principles.

Findings

Entropy depends on horizon area and spin-3 charge

Spin-3 charge has an upper bound related to horizon area

Formula reduces to known results in weak spin-3 limit

Abstract

A generic formula for the entropy of three-dimensional black holes endowed with a spin-3 field is found, which depends on the horizon area A and its spin-3 analogue, given by the reparametrization invariant integral of the induced spin-3 field at the spacelike section of the horizon. From this result it can be shown that the absolute value of the spin-3 analogue of the area has to be bounded from above by A/3^(1/2). The entropy formula is constructed by requiring the first law of thermodynamics to be fulfilled in terms of the global charges obtained through the canonical formalism. For the static case, in the weak spin-3 field limit, our expression for the entropy reduces to the result found by Campoleoni, Fredenhagen, Pfenninger and Theisen, which has been recently obtained through a different approach.