We perform the Hamiltonian reduction of three dimensional Einstein gravity with negative cosmological constant under constraints imposed by near horizon boundary conditions. The theory reduces to a Floreanini-Jackiw type scalar field theory on the horizon, where the scalar zero modes capture the global black hole charges. The near horizon Hamiltonian is a total derivative term, which explains the softness of all oscillator modes of the scalar field. We find also a (Korteweg-de Vries) hierarchy of modified boundary conditions that we use to lift the degeneracy of the soft hair excitations on the horizon.
Cited by 2
Emilio Ojeda et al., Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies
J. High Energ. Phys. 2019, 79 (2019) [Crossref]
Marc Henneaux et al., Asymptotic dynamics of AdS3 gravity with two asymptotic regions
J. High Energ. Phys. 2020, 64 (2020) [Crossref]
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- 1 Daniel Grumiller,
- 2 3 Wout Merbis
- 1 Technische Universität Wien / Vienna University of Technology [TUW]
- 2 International Solvay Institutes
- 3 Université Libre de Bruxelles [ULB]
- Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
- European Research Council [ERC]
- Fonds De La Recherche Scientifique - FNRS (FNRS) (through Organization: Fonds National de la Recherche Scientifique [FNRS])