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

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.

Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations

<abstract><p>We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the deterministic one, such as conditional, partial and asymptotic symmetries. A number of explicit examples are presented.</p></abstract>

Asymptotic symmetry of four dimensional Einstein-Yang-Mills and Einstein-Maxwell theory

Asymptotic symmetry plays an important role in determining physical observables of a theory. Recently, in the context of four dimensional asymptotically flat pure gravity and $$ \mathcal{N} $$ N = 1 supergravity, it has been proposed that OPEs of appropriate celestial amplitudes can be used to find their asymptotic symmetries. In this paper we find the asymptotic symmetry algebras of four dimensional Einstein-Yang-Mills and Einstein-Maxwell theories using this alternative approach, namely using the OPEs of their respective celestial amplitudes. The algebra obtained here are in agreement with the known results in the literature.

Asymptotic symmetries in Carrollian theories of gravity

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.

Higher Number of Yeast-like Fungi in the Air in 2018 after an Emergency Discharge of Raw Sewage to the Gulf of Gdańsk—Use of Contingency Tables

This study aimed to investigate the differences between the number of yeast-like fungi and molds in the coastal air of five coastal towns of the Gulf of Gdańsk in 2014–2017 vs. 2018, which saw an emergency discharge of sewage. In 2014–2017, a total of 62 duplicate samples were collected in the coastal towns of Hel, Puck, Gdynia, Sopot, and Gdańsk-Brzeźno. In 2018, after the emergency disposal of raw sewage, 26 air samples were collected. A Pearson chi-squared test of independence showed that during 2018 in Hel and Sopot, the mean number of molds and yeast-like fungi was higher than in 2014–2017. The result was significantly positive, p ≤ 2.22 × 10−16. The analysis of the General Asymptotic Symmetry Test showed that in Puck and Gdańsk-Brzeźno, the average number of Aspergillus sp. mold fungi was higher in 2018 after an emergency discharge of sewage into the Gulf of Gdańsk compared to the period 2014–2017. The result was not statistically significant. In addition, the average number of Penicillium sp. molds in 2018 in Gdańsk-Brzeźno was higher than in 2014–2017, but statistically insignificant (p = 0.9593). In 2018, the average number of Cladosporium sp. molds in Sopot was higher, but also statistically insignificant (p = 0.2114) compared to 2014–2017. Our results indicate that the study of the number of yeast-like fungi in the air may indicate coastal areas that may be particularly at risk of bacterial or mycological pathogens, e.g., after an emergency discharge of raw sewage.

Asymptotic symmetries of scalar electrodynamics and of the abelian Higgs model in Hamiltonian formulation

We investigate the asymptotic symmetry group of a scalar field minimally-coupled to an abelian gauge field using the Hamiltonian formulation. This extends previous work by Henneaux and Troessaert on the pure electromagnetic case. We deal with minimally coupled massive and massless scalar fields and find that they behave differently insofar as the latter do not allow for canonically implemented asymptotic boost symmetries. We also consider the abelian Higgs model and show that its asymptotic canonical symmetries reduce to the Poincaré group in an unproblematic fashion.

Flat space holography in spin-2 extended dilaton-gravity

We present an interacting spin-2 gauge theory coupled to the two-dimensional dilaton-gravity in flat spacetime. The asymptotic symmetry group is enhanced to the central extension of Diff(S1)⋉C∞(S1)⋉Vec(S1) when the central element of the Heisenberg subgroup is zero (vanishing U(1) level). Using the BF-formulation of the model we derive the corresponding boundary coadjoint action which is the spin-2 extension of the warped Schwarzian theory at vanishing U(1) level. We also discuss the thermodynamics of black holes in this model.

A note on Kerr/CFT and Wald entropy discrepancy in high derivative gravities

We examine the Kerr/CFT correspondence in Einstein gravity extended with quadratic curvature invariants. We consider two explicit examples in four and five dimensions and compute the central charges of the asymptotic symmetry algebras of the near horizon geometries, using the improved version of the BBC formalism that encompasses the information of the Lagrangian. We find that the resulting Cardy entropy differs from the Wald entropy, caused by the Riemann-squared RμνρσRμνρσ term.

Charge algebra in Al(A)dSn spacetimes

The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.