The integrability of Virasoro charges for axisymmetric Killing horizons

TL;DR

This paper investigates the conditions under which Virasoro charges are integrable on axisymmetric Killing horizons, revealing relationships between horizon temperatures and central charges with implications for black hole thermodynamics.

Contribution

It derives the integrability conditions for Virasoro generators on Killing horizons and explores their implications for dual CFT descriptions.

Findings

Integrability requires a specific relation between horizon temperatures.

When integrability holds for both horizons, the central charges are equal.

The results have implications for understanding black hole entropy and dual CFTs.

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.