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.
Highlights
JHEP04(2021)011 generators could be integrable Hamiltonians on the covariant phase space was left for future study
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
Summary
The symplectic structure of gravity on null hypersurface has a very elegant and simple form in terms of geometrical quantities [44,45,46,47,48,49,50,51]. In the spin-2 term, the configuration varible is given by the conformal metric γab of spacial cross-section and the conjugate moment can be identified as shear σab. For the spin-1 part, the configuration variable is the generator a of the null hypersurface, while the conjugate momentum is the twist ωa 1-form. The last term δ(κ H) is a total variation (exact form) on the field space Including it into the integration on H changes the polarization on the spin-0 piece of the symplectic potential. Such an exact form can be modified by adding a boundary term lb to the Lagrangian and does not influence the equation of motion.
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