The integrability of Virasoro charges for axisymmetric Killing horizons

Abstract

Through the analysis of null symplectic structure, we derive the condition for integrable Virasoro generators on the covariant phase space of axisymmetric Killing horizons. A weak boundary condition selects a special relationship between the two temperatures for the putative CFT. When the integrability is satisfied for both future and past horizons, the two central charges are equal. At the end we discuss the physical implications.

Conservation and Integrability in Lower-Dimensional Gravity

“…This non-integrability is often considered as an unpleasant property since it implies that the finite charge expressions depend on the particular path that one chooses to integrate on the solution space, which is a typical feature of a dissipative system. Several prescriptions have been proposed to isolate meaningful integrable parts in the charge expressions [13,[16][17][18][19][20][21][22]. These procedures require additional inputs in the theory, which rely on the context and the specific motivations.…”