Carroll structures, null geometry, and conformal isometries

Ciambelli, Luca; Leigh, Robert G.; Marteau, Charles; Petropoulos, P. Marios

doi:10.1103/physrevd.100.046010

Cited by 135 publications

(183 citation statements)

References 35 publications

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“…The relevance of such Ehresmann connections in the study of Carroll geometries on null surfaces [88] was recently emphasized in [89], so investigating the relationship between Carroll geometries and the near-horizon Virasoro symmetries may lead to a deeper understanding as to their fundamental origin. Note, however, it is important that the generators are defined to preserve C ab in a neighborhood of the bifurcation surface; it is not enough to simply find vector fields that preserve P + and P − on each of the respective horizons.…”

Section: Jhep01(2021)137mentioning

confidence: 99%

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

Chandrasekaran

Speranza

2021

J. High Energ. Phys.

175

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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.

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Section: Jhep01(2021)137mentioning

confidence: 99%

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

Chandrasekaran

Speranza

2021

J. High Energ. Phys.

175

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“…The Carrollian world emerged with the seminal work of Lévy-Leblond [43]. Although kinematically restricted due to the vanishing velocity of light (here k), the corresponding symmetry is as big as for Galilean systems, and provides a rich palette of mathematical [44][45][46][47][48][49][50][51][52][53][55][56][57] and physical [58][59][60][61][62][63] applications, mostly in relation with asymptotic symmetries of Ricci-flat gravitational backgrounds, and possibly with their holographic duals [64][65][66][67][68][69]. Assuming the latter exist, the study of their hydrodynamic regime calls for a theory of Carrollian fluids.…”

Section: Jhep11(2020)092mentioning

confidence: 99%

Gauges in three-dimensional gravity and holographic fluids

Ciambelli

Marteau

Petropoulos

et al. 2020

J. High Energ. Phys.

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Solutions to Einstein’s vacuum equations in three dimensions are locally maximally symmetric. They are distinguished by their global properties and their investigation often requires a choice of gauge. Although analyses of this sort have been performed abundantly, several relevant questions remain. These questions include the interplay between the standard Bondi gauge and the Eddington-Finkelstein type of gauge used in the fluid/gravity holographic reconstruction of these spacetimes, as well as the Fefferman-Graham gauge, when available i.e. in anti de Sitter. The goal of the present work is to set up a thorough dictionary for the available descriptions with emphasis on the relativistic or Carrollian holographic fluids, which portray the bulk from the boundary in anti-de Sitter or flat instances. A complete presentation of residual diffeomorphisms with a preliminary study of their algebra accompanies the situations addressed here.

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“…The flat limit leads therefore to a degenerate boundary metric. This is the well-known ultrarelativistic limit, named Carrollian in [59], and emerging generally as the geometry of null hypersurfaces (here null infinity) [61][62][63][64][65][66][67][68][69][70][71][72][73] (see also section 4.4). We can also define a density…”

Section: Pos(corfu2019)154mentioning

confidence: 99%

“…Mathematical and physical queries on the ultra-relativistic limit, dubbed Carrollian, started with the work of Lévy-Leblond[59], and gain attention over the recent years, often in conjunction with its dual Galilean counterpart[60][61][62][63][64][65][66][67][68][69][70][71][72][73] 5. Other methods for generalizing hydrodynamics on non-relativistic spacetimes can be found e.g.…”

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confidence: 99%

Fefferman--Graham and Bondi Gauges in the Fluid/Gravity Correspondence

Ciambelli¹,

Marteau²,

Petropoulos³

et al. 2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

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In three-dimensional gravity, we discuss the relation between the Fefferman-Graham gauge, the Bondi gauge and the Eddington-Finkelstein type of gauge, often referred to as the derivative expansion, involved in the fluid/gravity correspondence. Starting with a negative cosmological constant, for each gauge, we derive the solution space and the residual gauge diffeomorphisms. We construct explicitly the diffeomorphisms that relate the various gauges, and establish the precise matching of their boundary data. We show that Bondi and Fefferman-Graham gauges are equivalent, while the fluid/gravity derivative expansion, originating from a partial gauge fixing, exhibits an extra unspecified function that encodes the boundary fluid velocity. The Bondi gauge turns out to describe a subspace of the derivative expansion's solution space, featuring a fluid in a specific hydrodynamic frame. We pursue our analysis with the Ricci-flat limit of the Bondi gauge and of the fluid/gravity derivative expansion. The relations between them persist in this limit, which is well-defined and non-trivial. Moreover, the flat limit of the derivative expansion maps to the ultra-relativistic limit on the boundary. This procedure allows to unravel the holographic properties of the Bondi gauge for vanishing cosmological constant, in terms of its boundary Carrollian dual fluid.

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Carroll structures, null geometry, and conformal isometries

Cited by 135 publications

References 35 publications

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

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

Gauges in three-dimensional gravity and holographic fluids

Fefferman--Graham and Bondi Gauges in the Fluid/Gravity Correspondence

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