Boundary effects in General Relativity with tetrad variables

Oliveri, Roberto; Speziale, Simone

doi:10.1007/s10714-020-02733-8

Cited by 70 publications

(150 citation statements)

References 63 publications

Supporting

Mentioning

132

Contrasting

Order By: Relevance

“…We have also analyzed in details the simplicity constraints in this context, and presented the construction of the relative corner potential relating the Einstein-Cartan-Holst formulation to the ADM and Einstein-Hilbert metric formulations of gravity. These results reorganize in a coherent manner a large collection of disparate results in the literature on first order gravity and its symplectic potential [43,51,83,101,102,110,111,115,116,120,169,170].…”

Section: Resultsmentioning

confidence: 53%

“…We now give the explicit proof of the relationship between the bulk ECH potential and the GR potential. Similar relationships are given in [110,111,115,116], but here we establish them here in minute details. For this we have to consider the case σ = −1, but notice JHEP11(2020)027 that we could also take σ = +1 and compare with the Gibbons-Hawking potential Θ GH introduced in [1].…”

Section: Relationship Between Ech and Gr Potentialsmentioning

confidence: 67%

“…In this gauge, the gluing condition becomesẽ I S e I and there is no need to introduce independent corner fields different from the bulk ones. We can also recover the approach of [115,116]. What is done in these references can be interpreted in our framework as imposing strongly, independently of any corner Gauss law, the conditionẽ I S = e I in the extended symplectic potential.…”

Section: Trivial Limitsmentioning

confidence: 82%

“…Elements of this decomposition, including the central role of the internal normal on the corner phase space, have already appeared in the literature [43,83,101,102,[107][108][109][110][111][112][113][114][115][116], but here we put the pieces together and squeeze all the physical content out of this formula. For Lorentz transformations, the corner potential yields symmetry charges satisfying an sl(2, C) S algebra, 4 with the generators given by the corner 2-form…”

Section: Jhep11(2020)027mentioning

confidence: 99%

“…While it would seem that everybody agrees on these facts, there is a conceptual confusion on how to interpret them and deal with them. After all (continuing on the example of Lorentz transformations) one could proceed as in [115,116] and introduce the relative Θ DPS potential in order to cancel the Lorentz charges and thereby restore gauge invariance. But this restoration is then at the price of loosing access to the underlying charges, which is unfortunate since they give us an handle on quantization, and are the building blocks of the LQG quantization.…”

Section: Conceptual Motivationsmentioning

confidence: 99%

See 4 more Smart Citations

Edge modes of gravity. Part II. Corner metric and Lorentz charges

Freidel

Geiller

Pranzetti

2020

J. High Energ. Phys.

108

195

View full text Add to dashboard Cite

In this second paper of the series we continue to spell out a new program for quantum gravity, grounded in the notion of corner symmetry algebra and its representations. Here we focus on tetrad gravity and its corner symplectic potential. We start by performing a detailed decomposition of the various geometrical quantities appearing in BF theory and tetrad gravity. This provides a new decomposition of the symplectic potential of BF theory and the simplicity constraints. We then show that the dynamical variables of the tetrad gravity corner phase space are the internal normal to the spacetime foliation, which is conjugated to the boost generator, and the corner coframe field. This allows us to derive several key results. First, we construct the corner Lorentz charges. In addition to sphere diffeomorphisms, common to all formulations of gravity, these charges add a local $$ \mathfrak{sl} $$ sl (2, ℂ) component to the corner symmetry algebra of tetrad gravity. Second, we also reveal that the corner metric satisfies a local $$ \mathfrak{sl} $$ sl (2, ℝ) algebra, whose Casimir corresponds to the corner area element. Due to the space-like nature of the corner metric, this Casimir belongs to the unitary discrete series, and its spectrum is therefore quantized. This result, which reconciles discreteness of the area spectrum with Lorentz invariance, is proven in the continuum and without resorting to a bulk connection. Third, we show that the corner phase space explains why the simplicity constraints become non-commutative on the corner. This fact requires a reconciliation between the bulk and corner symplectic structures, already in the classical continuum theory. Understanding this leads inevitably to the introduction of edge modes.

show abstract

Section: Resultsmentioning

confidence: 53%

Section: Relationship Between Ech and Gr Potentialsmentioning

confidence: 67%

Section: Trivial Limitsmentioning

confidence: 82%

Section: Jhep11(2020)027mentioning

confidence: 99%

Section: Conceptual Motivationsmentioning

confidence: 99%

See 3 more Smart Citations

Edge modes of gravity. Part II. Corner metric and Lorentz charges

Freidel

Geiller

Pranzetti

2020

J. High Energ. Phys.

108

195

View full text Add to dashboard Cite

show abstract

Corner Symmetry and Quantum Geometry

Freidel,

Geiller,

Wieland

2023

Handbook of Quantum Gravity

View full text Add to dashboard Cite

Anomalies in gravitational charge algebras of null boundaries and black hole entropy

Chandrasekaran

Speranza

2021

J. High Energ. Phys.

175

View full text Add to dashboard Cite

We revisit the covariant phase space formalism applied to gravitational theories with null boundaries, utilizing the most general boundary conditions consistent with a fixed null normal. To fix the ambiguity inherent in the Wald-Zoupas definition of quasilocal charges, we propose a new principle, based on holographic reasoning, that the flux be of Dirichlet form. This also produces an expression for the analog of the Brown-York stress tensor on the null surface. Defining the algebra of charges using the Barnich-Troessaert bracket for open subsystems, we give a general formula for the central — or more generally, abelian — extensions that appear in terms of the anomalous transformation of the boundary term in the gravitational action. This anomaly arises from having fixed a frame for the null normal, and we draw parallels between it and the holographic Weyl anomaly that occurs in AdS/CFT. As an application of this formalism, we analyze the near-horizon Virasoro symmetry considered by Haco, Hawking, Perry, and Strominger, and perform a systematic derivation of the fluxes and central charges. Applying the Cardy formula to the result yields an entropy that is twice the Bekenstein-Hawking entropy of the horizon. Motivated by the extended Hilbert space construction, we interpret this in terms of a pair of entangled CFTs associated with edge modes on either side of the bifurcation surface.

show abstract

Boundary effects in General Relativity with tetrad variables

Cited by 70 publications

References 63 publications

Edge modes of gravity. Part II. Corner metric and Lorentz charges

Edge modes of gravity. Part II. Corner metric and Lorentz charges

Corner Symmetry and Quantum Geometry

Anomalies in gravitational charge algebras of null boundaries and black hole entropy

Contact Info

Product

Resources

About