Gravity degrees of freedom on a null surface

Hopfmüller, Florian; Freidel, Laurent

doi:10.1103/physrevd.95.104006

Cited by 71 publications

(139 citation statements)

References 26 publications

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“…In a Hamiltonian perspective, they are canonical conjugate of each other. Moreover, the canonical momenta satisfy constraint equations that are imposed by the gravitational dynamics [35,36]. The induced geometry on H is degenerate and reads…”

Section: Intrinsic and Extrinsic Geometry Of The Horizonmentioning

confidence: 99%

Carrollian physics at the black hole horizon

Donnay¹,

Marteau²

2019

Class. Quantum Grav.

175

109

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We show that the geometry of a black hole horizon can be described as a Carrollian geometry emerging from an ultra-relativistic limit where the near-horizon radial coordinate plays the role of a virtual velocity of light tending to zero. We prove that the laws governing the dynamics of a black hole horizon, the null Raychaudhuri and Damour equations, are Carrollian conservation laws obtained by taking the ultra-relativistic limit of the conservation of an energy-momentum tensor; we also discuss their physical interpretation. We show that the vector fields preserving the Carrollian geometry of the horizon, dubbed Carrollian Killing vectors, include BMS-like supertranslations and superrotations and that they have non-trivial associated conserved charges on the horizon. In particular, we build a generalization of the angular momentum to the case of nonstationary black holes. Finally, we discuss the relation of these conserved quantities to the infinite tower of charges of the covariant phase space formalism.

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Section: Intrinsic and Extrinsic Geometry Of The Horizonmentioning

confidence: 99%

Carrollian physics at the black hole horizon

Donnay¹,

Marteau²

2019

Class. Quantum Grav.

175

109

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“…For a careful treatment of caustics, corner data and residual diffeos, see [38,45], as well as [46] in a related context. For a more general expression of Θ without a full foliation and a discussion of corner terms without any coordinate gauge fixing, and its relevance to capture the full information about the charges, see [47]. See also [43,[48][49][50] for additional discussions on corner terms.…”

Section: Jhep11(2017)205mentioning

confidence: 99%

Sachs’ free data in real connection variables

Paoli

Speziale

2017

J. High Energ. Phys.

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Abstract:We discuss the Hamiltonian dynamics of general relativity with real connection variables on a null foliation, and use the Newman-Penrose formalism to shed light on the geometric meaning of the various constraints. We identify the equivalent of Sachs' constraint-free initial data as projections of connection components related to null rotations, i.e. the translational part of the ISO(2) group stabilising the internal null direction soldered to the hypersurface. A pair of second-class constraints reduces these connection components to the shear of a null geodesic congruence, thus establishing equivalence with the second-order formalism, which we show in details at the level of symplectic potentials. A special feature of the first-order formulation is that Sachs' propagating equations for the shear, away from the initial hypersurface, are turned into tertiary constraints; their role is to preserve the relation between connection and shear under retarded time evolution. The conversion of wave-like propagating equations into constraints is possible thanks to an algebraic Bianchi identity; the same one that allows one to describe the radiative data at future null infinity in terms of a shear of a (non-geodesic) asymptotic null vector field in the physical spacetime. Finally, we compute the modification to the spin coefficients and the null congruence in the presence of torsion.

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“…Hence these near horizon boundary conditions are also referred to as "Heisenberg boundary conditions". To see that (15) indeed corresponds to black hole solutions we should construct the metrics associated with these boundary conditions. First we write a t andā t proportional to a gauge transformation with arbitrary, state-independent parameters ζ ± .…”

Section: Near Horizon Boundary Conditionsmentioning

confidence: 99%

“…In [22] it was shown how the near horizon boundary conditions are related to the usual Brown-Henneaux boundary conditions with chemical potentials. Using slightly different conventions here, we map the near horizon boundary conditions a NH σ given by (15) to the Brown-Henneaux ones [a BH σ given in (107)] by a suitable gauge transformation g,…”

Section: Chiral Bosons Liouville Theory and Schwarzian Actionmentioning

confidence: 99%

“…Boundary charges also exist in the presence of finite boundaries, which can arise in two ways: either there is an actual boundary present in the physical system or one introduces a boundary by cutting out some part of spacetime, see for instance [14,15]. The prototypical example of the latter is to cut out the black hole interior and to replace the black hole by some membrane [16,17], corresponding to suitable boundary conditions imposed on a (stretched) horizon [18].…”

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confidence: 99%

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Near horizon dynamics of three dimensional black holes

Grumiller

Merbis

2020

SciPost Phys.

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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. Contents arXiv:1906.10694v2 [hep-th] 9 Jul 2019 SciPost Physics Submission B Gelfand-Dikii differential polynomials and Hamiltonians 24 References 26with a i max ,N denoting the number for the largest value of i = i max that leads to non-vanishing a i,N within a given set {a i,N }, and h {a i,N } are rational coefficients for each of these sets. Explicit results for N = 5, 6, 7 are H nl 5 = − 5 36 J 4 + 5 63 J 3H nl 6 = − 5 6

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Gravity degrees of freedom on a null surface

Cited by 71 publications

References 26 publications

Carrollian physics at the black hole horizon

Carrollian physics at the black hole horizon

Sachs’ free data in real connection variables

Near horizon dynamics of three dimensional black holes

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