New boundary variables for classical and quantum gravity on a null surface

Wieland, Wolfgang

doi:10.1088/1361-6382/aa8d06

Cited by 62 publications

(107 citation statements)

References 66 publications

Supporting

Mentioning

102

Contrasting

Order By: Relevance

“…The identification of the connection constraint-free data as null rotations means that the degrees of freedom form a group, albeit non-compact, hence one could try to use loop quantum gravity quantization techniques without introducing the Immirzi parameter. Some of the corner data, which we did not investigate here, have already be shown to lead to a quantization of the area [22,50,59]. A quantization of the connection description of the radiative degrees of freedom can lead to new insights both for loop quantum gravity and for asymptotic quantisations based on a Fock space.…”

Section: Jhep11(2017)205mentioning

confidence: 92%

See 1 more Smart Citation

Sachs’ free data in real connection variables

Paoli

Speziale

2017

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

Section: Jhep11(2017)205mentioning

confidence: 92%

“…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.

View full text Add to dashboard Cite

show abstract

“…So far, we have merely discussed and reorganised past results. The next step ahead is to present an action S[p ± , q ± |h] for certain dynamical fields p ± , q ± and fixed external sources h = [m a ] : δh = 0 such that the resulting boundary field equations return us 11 Since (ℓ a , m back the constraint equations (33a-33f) and (31a-31c) of general relativity on a null hypersurface. In this way, the constraint equations of general relativity on a null surface turn into actual dynamical field equations, thereby realising a quasi-local version of the holographic principle at the light front.…”

Section: Generating Functional and Boundary Field Theorymentioning

confidence: 99%

“…On a null hypersurface, and for the usual Dirichlet boundary conditions we need an analogue of the Gibbons -Hawking boundary term to cancel the connection variation from the bulk. In terms of complex variables, this boundary term is given by the integral [11]…”

Section: Kinetic Termmentioning

confidence: 99%

Generating functional for gravitational null initial data

Wieland

2019

Class. Quantum Grav.

Self Cite

View full text Add to dashboard Cite

A field theory on a three-dimensional manifold is introduced, whose field equations are the constraint equations for general relativity on a three-dimensional null hypersurface. The underlying boundary action consists of two copies of the dressed Chern -Simons term for self-dual Ashtekar variables, a kinetic term for the null flag at the boundary plus additional junction conditions for the spin coefficients across the interface. In fact, there is a doubling of the field content, because the null hypersurface will be considered as an internal boundary between two adjacent slabs of spacetime. The paper concludes with a proposal for a construction of the gravitational transition amplitudes in the bulk via the auxiliary boundary field theory alone, namely by gluing amplitudes for edge states across two-dimensional corners, thus providing a proposal for a quasi-local realisation of the holographic principle at the light front.

show abstract

“…Null boundaries are particularly important as they play a fundamental role in gravitational thermodynamics [11][12][13][14], as well as in holography and quantum gravity [15][16][17]. Moreover, it was recently conjectured that the symmetries and charges at stationary event horizons is relevant to the black hole information problem [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Symmetries, charges and conservation laws at causal diamonds in general relativity

Chandrasekaran

Prabhu

2019

J. High Energ. Phys.

View full text Add to dashboard Cite

We study the covariant phase space of vacuum general relativity at the null boundary of causal diamonds. The past and future components of such a null boundary each have an infinite-dimensional symmetry algebra consisting of diffeomorphisms of the 2-sphere and boost supertranslations corresponding to angle-dependent rescalings of affine parameter along the null generators. Associated to these symmetries are charges and fluxes obtained from the covariant phase space formalism using the prescription of Wald and Zoupas. By analyzing the behavior of the spacetime metric near the corners of the causal diamond, we show that the fluxes are also Hamiltonian generators of the symmetries on the phase space. In particular, the supertranslation fluxes yield an infinite family of boost Hamiltonians acting on the gravitational data of causal diamonds. We show that the smoothness of the vector fields representing such symmetries at the bifurcation edge of the causal diamond implies suitable matching conditions between the symmetries on the past and future components of the null boundary. Similarly, the smoothness of the spacetime metric implies that the fluxes of all such symmetries is conserved between the past and future components of the null boundary. This establishes an infinite set of conservation laws for finite subregions in gravity analogous to those at null infinity. We also show that the symmetry algebra at the causal diamond has a non-trivial center corresponding to constant boosts. The central charges associated to these constant boosts are proportional to the area of the bifurcation edge, for any causal diamond, in analogy with the Wald entropy formula.

show abstract

New boundary variables for classical and quantum gravity on a null surface

Cited by 62 publications

References 66 publications

Sachs’ free data in real connection variables

Sachs’ free data in real connection variables

Generating functional for gravitational null initial data

Symmetries, charges and conservation laws at causal diamonds in general relativity

Contact Info

Product

Resources

About