Higher spin black hole entropy in three dimensions

Understand

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.