scholarly journals Extensions of the asymptotic symmetry algebra of general relativity

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Éanna É. Flanagan ◽  
Kartik Prabhu ◽  
Ibrahim Shehzad
Keyword(s):  
General Relativity ◽  
Symmetry Algebra ◽  
Asymptotic Symmetry

scholarly journals Asymptotic symmetries in Carrollian theories of gravity

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Alfredo Pérez
Keyword(s):  
General Relativity ◽  
Symmetry Algebra ◽  
Einstein Gravity ◽  
Point Of View ◽  
Asymptotic Symmetry ◽  
Gravitational Theories ◽  
Theories Of Gravity ◽  
Spatial Rotations ◽  
Lapse Function ◽  
Asymptotic Symmetries

Abstract Asymptotic symmetries in Carrollian gravitational theories in 3+1 space and time dimensions obtained from “magnetic” and “electric” ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions are needed to guarantee a finite symplectic term, in analogy with Einstein gravity. For the magnetic contraction, when Regge-Teitelboim parity conditions are imposed, the asymptotic symmetries are described by the Carroll group. With Henneaux-Troessaert parity conditions, the asymptotic symmetry algebra corresponds to a BMS-like extension of the Carroll algebra. For the electric contraction, because the lapse function does not appear in the boundary term needed to ensure a well-defined action principle, the asymptotic symmetry algebra is truncated, for Regge-Teitelboim parity conditions, to the semidirect sum of spatial rotations and spatial translations. Similarly, with Henneaux-Troessaert parity conditions, the asymptotic symmetries are given by the semidirect sum of spatial rotations and an infinite number of parity odd supertranslations. Thus, from the point of view of the asymptotic symmetries, the magnetic contraction can be seen as a smooth limit of General Relativity, in contrast to its electric counterpart.

Kleinian characterization of asymptotic symmetries of real general relativity

1993 ◽  
Vol 441 (1913) ◽  
pp. 465-471 ◽  
Keyword(s):  
General Relativity ◽  
Automorphism Group ◽  
Group Action ◽  
Radon Transform ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
The Real ◽  
The Given ◽  
Asymptotic Symmetries

According to Klein’s Erlanger programme, one may (indirectly) specify a geometry by giving a group action. Conversely, given a group action, one may ask for the corresponding geometry. Recently, I showed that the real asymptotic symmetry groups of general relativity (in any signature) have natural ‘projective’ classical actions on suitable ‘Radon transform’ spaces of affine 3-planes in flat 4-space. In this paper, I give concrete models for these groups and actions. Also, for the ‘atomic’ cases, I give geometric structures for the spaces of affine 3-planes for which the given actions are the automorphism group.

scholarly journals Canonical charges and asymptotic symmetry algebra of conformal gravity

2015 ◽  
Vol 91 (10) ◽  
Author(s):  
Maria Irakleidou ◽  
Iva Lovrekovic ◽  
Florian Preis
Keyword(s):  
Symmetry Algebra ◽  
Conformal Gravity ◽  
Asymptotic Symmetry

scholarly journals Lie theory for asymptotic symmetries in general relativity: The BMS Group

2022 ◽  
Author(s):  
David Nicolas Prinz ◽  
Alexander Schmeding
Keyword(s):  
General Relativity ◽  
Lie Group ◽  
Group Structure ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
Infinite Dimensional ◽  
Real Analytic ◽  
Definition Of ◽  
Future Work ◽  
Asymptotic Symmetries

Abstract We study the Lie group structure of asymptotic symmetry groups in General Relativity from the viewpoint of infinite-dimensional geometry. To this end, we review the geometric definition of asymptotic simplicity and emptiness due to Penrose and the coordinate-wise definition of asymptotic flatness due to Bondi et al. Then we construct the Lie group structure of the Bondi--Metzner--Sachs (BMS) group and discuss its Lie theoretic properties. We find that the BMS group is regular in the sense of Milnor, but not real analytic. This motivates us to conjecture that it is not locally exponential. Finally, we verify the Trotter property as well as the commutator property. As an outlook, we comment on the situation of related asymptotic symmetry groups. In particular, the much more involved situation of the Newman--Unti group is highlighted, which will be studied in future work.

scholarly journals Exploring new boundary conditions for $$\mathcal {N}=(1,1)$$ extended higher-spin $$AdS_3$$ supergravity

2020 ◽  
Vol 80 (11) ◽  
Author(s):  
H. T. Özer ◽  
Aytül Filiz
Keyword(s):  
Boundary Conditions ◽  
Symmetry Algebra ◽  
General Boundary ◽  
Gauge Fields ◽  
General Boundary Conditions ◽  
Asymptotic Symmetry ◽  
Affine Algebra ◽  
Supersymmetric Extension ◽  
Higher Spin

AbstractIn this paper, we present a candidate for $$\mathcal {N}=(1,1)$$ N = ( 1 , 1 ) extended higher-spin $$AdS_3$$ A d S 3 supergravity with the most general boundary conditions discussed by Grumiller and Riegler recently. We show that the asymptotic symmetry algebra consists of two copies of the $$\mathfrak {osp}(3|2)_k$$ osp ( 3 | 2 ) k affine algebra in the presence of the most general boundary conditions. Furthermore, we impose some certain restrictions on gauge fields on the most general boundary conditions and that leads us to the supersymmetric extension of the Brown–Henneaux boundary conditions. We eventually see that the asymptotic symmetry algebra reduces to two copies of the $$\mathcal {SW}(\frac{3}{2},2)$$ SW ( 3 2 , 2 ) algebra for $$\mathcal {N}=(1,1)$$ N = ( 1 , 1 ) extended higher-spin supergravity.

scholarly journals Gravitational edge modes, coadjoint orbits, and hydrodynamics

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
William Donnelly ◽  
Laurent Freidel ◽  
Seyed Faroogh Moosavian ◽  
Antony J. Speranza
Keyword(s):  
General Relativity ◽  
Boundary Surface ◽  
Infinite Family ◽  
Symmetry Algebra ◽  
Complete Classification ◽  
Coadjoint Orbits ◽  
Poincaré Group ◽  
Poincare Group ◽  
Dimensional Group

Abstract The phase space of general relativity in a finite subregion is characterized by edge modes localized at the codimension-2 boundary, transforming under an infinite-dimensional group of symmetries. The quantization of this symmetry algebra is conjectured to be an important aspect of quantum gravity. As a step towards quantization, we derive a complete classification of the positive-area coadjoint orbits of this group for boundaries that are topologically a 2-sphere. This classification parallels Wigner’s famous classification of representations of the Poincaré group since both groups have the structure of a semidirect product. We find that the total area is a Casimir of the algebra, analogous to mass in the Poincaré group. A further infinite family of Casimirs can be constructed from the curvature of the normal bundle of the boundary surface. These arise as invariants of the little group, which is the group of area-preserving diffeomorphisms, and are the analogues of spin. Additionally, we show that the symmetry group of hydrodynamics appears as a reduction of the corner symmetries of general relativity. Coadjoint orbits of both groups are classified by the same set of invariants, and, in the case of the hydrodynamical group, the invariants are interpreted as the generalized enstrophies of the fluid.

scholarly journals Extended super BMS algebra of celestial CFT

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Angelos Fotopoulos ◽  
Stephan Stieberger ◽  
Tomasz R. Taylor ◽  
Bin Zhu
Keyword(s):  
Energy Momentum Tensor ◽  
Symmetry Algebra ◽  
Momentum Tensor ◽  
Wave Functions ◽  
Primary Wave ◽  
Asymptotic Symmetry ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Conformal Field ◽  
Super Symmetry

Abstract We study two-dimensional celestial conformal field theory describing four- dimensional $$ \mathcal{N} $$ N =1 supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of BMS symmetry. We construct fermionic conformal primary wave functions and show how they are related via supersymmetry to their bosonic partners. We use soft and collinear theorems of supersymmetric Einstein-Yang- Mills theory to derive the OPEs of the operators associated to massless particles. The bosonic and fermionic soft theorems are shown to form a sequence under supersymmetric Ward identities. In analogy with the energy momentum tensor, the supercurrents are shadow transforms of soft gravitino operators and generate an infinite-dimensional super- symmetry algebra. The algebra of $$ {\mathfrak{sbms}}_4 $$ sbms 4 generators agrees with the expectations based on earlier work on the asymptotic symmetry group of supergravity. We also show that the supertranslation operator can be written as a product of holomorphic and anti-holomorphic supercurrents.

scholarly journals Asymptotic symmetry algebra of conformal gravity

2017 ◽  
Vol 96 (10) ◽  
Author(s):  
Maria Irakleidou ◽  
Iva Lovrekovic
Keyword(s):  
Symmetry Algebra ◽  
Conformal Gravity ◽  
Asymptotic Symmetry
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