Pure mathematics

Algebra over a field

Phase space

Mathematics

Mathematical physics

Black hole thermodynamics

Computer science

Cellular algebra

Virasoro algebra

Quantum mechanics

Rotating black hole

Homogeneous space

Entropy (arrow of time)

Routing (electronic design automation)

Covariant transformation

Conformal map

Central charge

Black hole (networking)

Link-state routing protocol

Algebra representation

Angular momentum

Geometry

Routing protocol

Physics

Computer network

Journal of High Energy Physics

A bstract A set of infinitesimal Virasoro L ⊗ Virasoro R diffeomorphisms are presented which act non-trivially on the horizon of a generic Kerr black hole with spin J. The covariant phase space formalism provides a formula for the Virasoro charges as surface integrals on the horizon. Integrability and associativity of the charge algebra are shown to require the inclusion of ‘Wald-Zoupas’ counterterms. A counterterm satisfying the known consistency requirement is constructed and yields central charges c L = c R = 12 J . Assuming the existence of a quantum Hilbert space on which these charges generate the symmetries, as well as the applicability of the Cardy formula, the central charges reproduce the macroscopic area-entropy law for generic Kerr black holes.

Black hole entropy and soft hair