v2: added appendix on spatially open case; typos corrected and references updated (accepted in PRD) v1: 32 pages + one appendix + one figure (in this article we also review the notion of asymptotically flat spacetimes)
Null infinity in asymptotically flat spacetimes posses a rich mathematical structure; including the BMS group and the Bondi news tensor that allow one to study gravitational radiation rigorously. However, FLRW spacetimes are not asymptotically flat because their stress-energy tensor does not decay sufficiently fast and in fact diverges at null infinity. This class includes matter- and radiation-dominated FLRW spacetimes. We define a class of spacetimes whose structure at null infinity is similar to FLRW spacetimes: the stress-energy tensor is allowed to diverge and the conformal factor is not smooth at null infinity. Interestingly, for this larger class of spacetimes, the asymptotic symmetry algebra is similar to the BMS algebra but not isomorphic to it. In particular, the symmetry algebra is the semi-direct sum of supertranslations and the Lorentz algebra, but it does not have any preferred translation subalgebra. Future applications include studying gravitational radiation in FLRW the full nonlinear theory, including the cosmological memory effect, and also asymptotic charges in this framework.
We describe a novel twistorial construction of the asymptotic BMS symmetries at null infinity for asymptotically flat spacetimes. We define BMS twistors as spinor solutions to some set of components of the usual spacetime twistor equation restricted to null infinity. The space of BMS twistors is infinite-dimensional. We show that given two BMS twistors their symmetric tensor product can be used to generate (complex) vector fields which are the infinitesimal BMS symmetries of null infinity. In this sense BMS twistors are "square roots" of BMS symmetries. We also show that these BMS twistor equa…
We show that we can combine the (complex, self-dual) BMS vector fields with the recently defined BMS twistors to obtain a new supersymmetric extension of the BMS symmetries at null infinity. We compare our construction to other supersymmetric extensions of the BMS algebra proposed in the context of supergravity. Unlike the standard constructions the anticommutator in our superalgebra generates all the BMS vector fields including the Lorentz transformations. We also show that there exists a projection from our BMS Lie superalgebra to the global subalgebra of the Neveu-Schwarz supersymmetries on…
BMS symmetry is a symmetry of asymptotically flat spacetimes in the vicinity of the null boundary of spacetime and it is expected to play a fundamental role in physics. It is interesting therefore to investigate the structures and properties of quantum deformations of these symmetries, which are expected to shed some light on symmetries of quantum spacetime. In this paper we discuss the structure of the algebra of extended BMS symmetries in 3 and 4 spacetime dimensions, realizing that these algebras contain an infinite number of distinct Poincaré subalgebras, a fact that has previously been no…
The Bondi-van der Burg-Metzner-Sachs (BMS) group is the asymptotic symmetry group of asymptotically flat gravity. Recently, Donnay et al. have derived an analogous symmetry group acting on black hole event horizons. For a certain choice of boundary conditions, it is a semidirect product of ${\rm Diff}(S^2)$, the smooth diffeomorphisms of the two-sphere, acting on $C^\infty(S^2)$, the smooth functions on the two-sphere. We observe that the same group appears in fluid dynamics as symmetries of the compressible Euler equations. We relate these two realizations of ${\rm Diff}(S^2)\ltimes C^\infty(…
Institut Denis Poisson, Université de Tours, Université d’Orléans, CNRS（德尼·普瓦松研究所，图尔大学，奥尔良大学，法国国家科学研究中心）；Physique de l’Univers, Champs et Gravitation, Université de Mons – UMONS（宇宙、场与引力物理系，蒙斯大学）
It is now well understood that Ward identities associated to the (extended) BMS algebra are equivalent to single soft graviton theorems. In this work, we show that if we consider nested Ward identities constructed out of two BMS charges, a class of double soft factorization theorems can be recovered. By making connections with earlier works in the literature, we argue that at the sub-leading order, these double soft graviton theorems are the so-called consecutive double soft graviton theorems. We also show how these nested Ward identities can be understood as Ward identities associated to BMS …
We study horizon shells and soldering freedom for extreme black holes and how supertranslation-like Bondi-Metzner-Sachs (BMS) symmetries appear as soldering transformations. Further, for a null shell placed infinitesimally close to the horizon of an extreme Reissner-Nordstr$\ddot{o}$m (RN) black hole, we show superrotation-like symmetries also arise as soldering freedom. Next, considering the interaction of impulsive gravitational waves supported at the horizon shell with test particles, we study how the "memory" (or the imprints) of BMS-like symmetries gets encoded in the geodesics (test part…
This article reviews one of the most intriguing properties of black hole spacetimes known in the literature -- gravitational memory effect, and its connection with asymptotic symmetries, also termed as Bondi-van der Burg-Metzner-Sachs (BMS) symmetries, emerging near the horizon of black holes. Gravitational memory is a non-oscillatory part of the gravitational wave amplitude which generates a permanent displacement for freely falling test particles or test detectors. We highlight a model scenario where asymptotic symmetries appear as a soldering freedom in the context of stitching of two black…
Symmetries play an interesting role in cosmology. They are useful in characterizing the cosmological perturbations generated during inflation and lead to consistency relations involving the soft limit of the statistical correlators of large-scale structure dark matter and galaxies overdensities. On the other hand, in observational cosmology the carriers of the information about these large-scale statistical distributions are light rays traveling on null geodesics. Motivated by this simple consideration, we study the structure of null infinity and the associated BMS symmetry in a cosmological s…
We consider a BMS-type symmetry action on isolated horizons in asymptotically flat spacetimes. From the viewpoint of the non-relativistic field theory on a horizon membrane, supertranslations shift the field theory spatial momentum. The latter is related by a Ward identity to the particle number symmetry current and is spontaneously broken. The corresponding Goldstone boson shifts the horizon angular momentum and can be detected quantum mechanically. Similarly, area preserving superrotations are spontaneously broken on the horizon membrane and we identify the corresponding gapless modes. In as…
These notes are an introduction to asymptotic symmetries in gauge theories, with a focus on general relativity in four dimensions. We explain how to impose consistent sets of boundary conditions in the gauge fixing approach and how to derive the asymptotic symmetry parameters. The different procedures to obtain the associated charges are presented. As an illustration of these general concepts, the examples of four-dimensional general relativity in asymptotically (locally) (A)dS$_4$ and asymptotically flat spacetimes are covered. This enables us to discuss the different extensions of the Bondi-…
Cataclysmic astrophysical phenomena can produce impulsive gravitational waves that can possibly be detected by the advanced versions of present-day detectors in the future. Gluing of two spacetimes across a null surface produces impulsive gravitational waves (in the phraseology of Penrose [1]) having a Dirac Delta function type pulse profile along the surface. It is known that BMS-like symmetries appear as soldering freedom while we glue two spacetimes along a null surface. In this note, we study the effect of such impulsive gravitational waves on test particles (detectors) or geodesics. We sh…
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. Fina…
The asymptotic group of symmetries at null infinity of flat spacetimes in three and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS) group. This has recently been shown to be isomorphic to non-relativistic conformal algebras in one lower dimension, the Galilean Conformal Algebra (GCA) in 2d and a closely related non-relativistic algebra in 3d [1]. We provide a better understanding of this surprising connection by providing a spacetime interpretation in terms of a novel contraction. The 2d GCA, obtained from a linear combination of two copies of the Virasoro algebra, is gen…
The Poisson brackets of the gravitational field at null infinity play a pivotal role in establishing the equivalence between the Ward identities involving BMS charges and the soft graviton theorem. In recent literature it was noticed that, in order to reproduce the action of BMS transformations via such Poisson brackets, one needs to add "ad-hoc" boundary terms in the symplectic form. In this note we show that, introducing a suitable splitting of the gravitational field in bulk and boundary degrees of freedom and using techniques of covariant phase space formalism, it is possible to obtain the…
Motivated by the equivalence between soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the BMS group, we propose a new extension (different from the so-called extended BMS) of the BMS group which is a semi-direct product of supertranslations and Diff(S^2). We propose a definition for the canonical generators associated to the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.
BMS group (and it's various generalizations) at null infinity have been studied extensively in the literature as the symmetry group of asymptotically flat spacetimes. The intricate relationship between soft theorems and the BMS symmetries have also motivated the definition of such asymptotic symmetries to time-like infinity. Although the vector fields that generate the (generalized) BMS algebra at time-like infinity was defined in the literature, the algebra has not been investigated. In this paper, we fill this gap. We show that the super-translations and vector fields that generate sphere di…
We show that the asymptotic infinite dimensional enlarged gauge symmetries constructed for QED are anomalous in Dirac and Weyl semimetals. This symmetry is particularly important in particle physics for its analogy with the Bondi-Metzner-Sachs (BMS) symmetries in gravity, as well as for its connection with QED soft IR theorems. This leads to observable effects, because of the induction of a new current in the material, which carries a memory of the BMS symmetry precursor.
We explore the holographic principle in the context of asymptotically flat spacetimes. In analogy with the AdS/CFT scenario we analyse the asympotically symmetry group of this class of spacetimes, the so called Bondi-Metzner-Sachs (BMS) group. We apply the covariant entropy bound to relate bulk entropy to boundary symmetries and find a quite different picture with respect to the asymptotically AdS case. We then derive the covariant wave equations for fields carrying BMS representations to investigate the nature of the boundary degrees of freedom. We find some similarities with 't Hooft S-matri…
In a previous paper (hep-th/0306142) we have started to explore the holographic principle in the case of asymptotically flat space-times and analyzed in particular different aspects of the Bondi-Metzner-Sachs (BMS) group, namely the asymptotic symmetry group of any asymptotically flat space-time. We continue this investigation in this paper. Having in mind a S-matrix approach with future and past null infinity playing the role of holographic screens on which the BMS group acts, we connect the IR sectors of the gravitational field with the representation theory of the BMS group. We analyze the …
The conformal symmetry algebra in 2D (Diff($S^{1}$)$\oplus$Diff($S^{1}$)) is shown to be related to its ultra/non-relativistic version (BMS$_{3}$$\approx$GCA$_{2}$) through a nonlinear map of the generators, without any sort of limiting process. For a generic classical CFT$_{2}$, the BMS$_{3}$ generators then emerge as composites built out from the chiral (holomorphic) components of the stress-energy tensor, $T$ and $\bar{T}$, closing in the Poisson brackets at equal time slices. Nevertheless, supertranslation generators do not span Noetherian symmetries. BMS$_{3}$ becomes a bona fide symmetry…
When two spacetimes are stitched across a null-shell placed at the horizon of a black hole BMS-supertranslation like soldering freedom arises if one demands the induced metric on the horizon shell should remain invariant under the translations generated by the null generators of the shell. We revisit this phenomenon at the horizon of rotating shells and obtain BMS like symmetries. We further show that superrotation like soldering symmetries in the form of conformal isometries can emerge whenever the degenerate metric of any null hypersurface admits a dependency on null (degenerate direction) c…
Near the horizon, the obvious symmetries of a black hole spacetime---the horizon-preserving diffeomorphisms---are enhanced to a larger symmetry group with a BMS${}_3$ algebra. Using dimensional reduction and covariant phase space techniques, I investigate this augmented symmetry, and show that it is strong enough to determine the black hole entropy.
Starting from gravity in asymptotically flat spacetime, the BMS momentum fluxes are constructed. These are non-local expressions of the solution space living on the celestial Riemann surface. They transform in the coadjoint representation of the extended BMS group and correspond to Virasoro primaries under the action of bulk superrotations. The relation between the BMS momentum fluxes and celestial CFT operators is then established: the supermomentum flux is related to the supertranslation operator and the super angular momentum flux is linked to the stress-energy tensor of the celestial CFT. …
With a view to understanding extended-BMS symmetries in the framework of the $AdS_4/CFT_3$ correspondence, asymptotically AdS geometries are constructed with null impulsive shockwaves involving a discontinuity in superrotation parameters. The holographic dual is proposed to be a two-dimensional Euclidean defect conformal field localized on a particular timeslice in a three-dimensional conformal field theory on de Sitter spacetime. The defect conformal field theory generates a natural action of the Virasoro algebra. The large radius of curvature limit $\ell\to\infty$ yields spacetimes with nont…
The surface charges associated with the symmetries of asymptotically flat four dimensional spacetimes at null infinity are constructed. They realize the symmetry algebra in general only up to a field-dependent central extension that satisfies a suitably generalized cocycle condition. This extension vanishes when using the globally well defined BMS algebra. For the Kerr black hole and the enlarged BMS algebra with both supertranslations and superrotations, some of the supertranslations charges diverge whereas there are no divergences for the superrotation charges. The central extension is propo…
We revisit the status of asymptotic symmetries in higher even dimensions and propose a definition of superrotation charge beyond linearized gravity. We prove that there is a well-defined spacetime action of the superrotation charge on the space of asymptotically flat geometries. Additionally, we demonstrate that the Ward identity associated with superrotation charges follows from the subleading soft graviton theorem, which is a universal constraint (in $d> 4$) along with the leading soft graviton theorem.
New boundary conditions for asymptotically flat spacetimes are given at spatial infinity. These boundary conditions are invariant under the BMS group, which acts non trivially. The boundary conditions fulfill all standard consistency requirements: (i) they make the symplectic form finite; (ii) they contain the Schwarzchild solution, the Kerr solution and their Poincaré transforms, (iii) they make the Hamiltonian generators of the asymptotic symmetries integrable and well-defined (finite). The boundary conditions differ from the ones given earlier in the literature in the choice of the parity c…
Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these "maximally symmetric" spacetimes by investigating their local geometry. For each such spacetime and relative to exponential coordinates, we calculate the (infinitesimal) action of the kinematical symmetries, paying particular attention to the action of the boosts, showing in almost all cases that they act with generic non-compact orbits. We also calculate the soldering form, the associated viel…
We present a new set of asymptotic conditions for gravity at spatial infinity that includes gravitational magnetic-type solutions, allows for a non-trivial Hamiltonian action of the complete $BMS_4$ algebra, and leads to a non-divergent behaviour of the Weyl tensor as one approaches null infinity. We then extend the analysis to the coupled Einstein-Maxwell system and obtain as canonically realized asymptotic symmetry algebra a semi-direct sum of the $BMS_4$ algebra with the angle dependent $u(1)$ transformations. The Hamiltonian charge-generator associated with each asymptotic symmetry element…
It has been argued that the symmetries of gravity at null infinity should include a Diff$(S^2)$ factor associated to diffeomorphisms on the celestial sphere. However, the standard phase space of gravity does not support the action of such transformations. Building on earlier work by Laddha and one of the authors, we present an extension of the phase space of gravity at null infinity on which Diff$(S^2)$ acts canonically. The Poisson brackets of supertranslation and Diff$(S^2)$ charges reproduce the generalized BMS algebra introduced in arXiv:1408.2228 .
We study the Newman--Unti (NU) group from the viewpoint of infinite-dimensional geometry. The NU group is a topological group in a natural coarse topology, but it does not become a manifold and hence a Lie group in this topology. To obtain a manifold structure we consider a finer Whitney-type topology. This turns the unit component of the NU group into an infinite-dimensional Lie group. We then study the Lie theoretic properties of this group. Surprisingly, the group operations of the full NU group become discontinuous, whence the NU group does not support a Lie group structure. The NU group c…
We show that there exists an infinite tower of fermionic symmetries in pure $d=4$, $\mathcal{N}=1$ supergravity on an asymptotically flat background. The Ward identities associated with these symmetries are equivalent to the soft limit of the gravitino and to the statement of supersymmetry at every angle. Additionally, we show that these charges commute into charges associated with the (unextended) BMS group, providing a supersymmetrization of the BMS translations.
A consistent set of asymptotic conditions for the simplest supergravity theory without cosmological constant in three dimensions is proposed. The canonical generators associated to the asymptotic symmetries are shown to span a supersymmetric extension of the BMS$_3$ algebra with an appropriate central charge. The energy is manifestly bounded from below with the ground state given by the null orbifold or Minkowski spacetime for periodic, respectively antiperiodic boundary conditions on the gravitino. These results are related to the corresponding ones in AdS$_3$ supergravity by a suitable flat …
We study a three-dimensional Chern-Simons gravity theory based on the Maxwell algebra. We find that the boundary dynamics is described by an enlargement and deformation of the $\mathfrak{bms}_3$ algebra with three independent central charges. This symmetry arises from a gravity action invariant under the local Maxwell group and is characterized by presence of Abelian generators which modify the commutation relations of the super-translations in the standard $\mathfrak{bms}_3$ algebra. Our analysis is based on the charge algebra of the theory in the BMS gauge, which includes the known solutions…
We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS$_{3}$ algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis is performed in terms of two-dimensional gauge fields for $isl(2,R)$. Although the algebra is not semisimple, the formulation can be carried out à la Drinfeld-Sokolov because it admits a nondegenerate invariant bilinear metric. The hierarchy turns out to be bi-Hamiltonian, labeled by a nonnegative integer $k$, and defined through a suitable generalization of …
After a review of symmetries and classical solutions involved in the AdS3/CFT2 correspondence, we apply a similar analysis to asymptotically flat spacetimes at null infinity in 3 and 4 dimensions. In the spirit of two dimensional conformal field theory, the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions is taken to be the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a first application, we derive how the symmetry algebra is realized on solution space. In partic…
We investigate the standard and dual Bondi-Metzner-Sachs (BMS) supertranslation generators on a black hole horizon and draw some conclusions about black hole physics. Recently, it has been shown that in addition to conventional BMS supertranslation symmetries, there exists an additional infinite set of magnetic asymptotic symmetries, dual BMS supertranslations, again parametrized by a function on the two-sphere. We show that the Dirac bracket between these generators exhibits an anomalous central term when one parameter function exhibits a singularity in the complex stereographical coordinates…
We show that in scalar-field cosmology, a dust fluid follows as quantum corrections from solutions of the Wheeler-DeWitt equation generated by Lie symmetries. The energy density of the dust fluid is related with the frequency of the wavefunction.
Super-BMS$_4$ algebras -- also called BMS$_4$ superalgebras -- are graded extensions of the BMS$_4$ algebra. They can be of two different types: they can contain either a finite number or an infinite number of fermionic generators. We show in this letter that, with suitable boundary conditions on the graviton and gravitino fields at spatial infinity, supergravity on asymptotically flat spaces possesses as superalgebra of asymptotic symmetries a (nonlinear) super-BMS$_4$ algebra containing an infinite number of fermionic generators, which we denote SBMS$_4$. These boundary conditions are not on…
Following the recent work of Henneaux and Troessaert, which revisits the problem of spacetime symmetries at spatial infinity, we analyze this problem using the Bondi metric without determinant condition as our starting point. It turns out that in this case the symmetries at spatial infinity form the BMS symmetry appended with an additional infinite set of abelian symmetries. We furthermore find that imposing the determinant condition to the Bondi metric would result in a drastic reduction of symmetries, with no spatial (super) translations present.
In [15] we proposed a generalization of the BMS group G which is a semidirect product of supertranslations and smooth diffeomorphisms of the conformal sphere. Although an extension of BMS, G is a symmetry group of asymptotically flat space times. By taking G as a candidate symmetry group of the quantum gravity S-matrix, we argued that the Ward identities associated to the generators of Diff(S^2) were equivalent to the Cachazo-Strominger subleading soft graviton theorem. Our argument however was based on a proposed definition of the Diff(S^2) charges which we could not derive from first princip…
Recently it has been shown that there is asymptotic BMS-like symmetry associated with the near-horizon geometry of black holes in three and four dimensions. In this paper, we show that the presence of such BMS-like symmetry is a ubiquitous feature for black holes in generic dimensions. For black holes in $D$ dimensions, the symmetry contains 2 supertranslations and $D-2$ generalized superrotations. The superrotations are found to generate a generalized Witt-like algebra that was previously noticed in a rather different construction. In the case of stationary and axisymmetric black holes, we ca…
We show that the symmetry algebra of asymptotically flat four dimensional spacetimes at null infinity in the sense of Newman and Unti is isomorphic to the direct sum of the abelian algebra of infinitesimal conformal rescalings with bms4. We then work out the local conformal properties of the relevant Newman-Penrose coefficients, as well as the surface charges and their algebra.
We study the Lie point symmetries of Einstein's equations for the Friedmann-Roberstson-Walker Cosmology. They form either a two - dimensional or a three - dimensional solvable group depending on the form of the self interacting potential. Using the invariants of the group we reduce the second order system of differential equations into a first order system. Writing the action in terms of the proper time we study the point symmetries and the variational symmetries of the resulting equations.
We present a definition of null G-structures on Lorentzian manifolds and investigate their geometric properties. This definition includes the Robinson structure on 4-dimensional black holes as well as the null structures that appear in all supersymmetric solutions of supergravity theories. We also identify the induced geometry on some null hypersurfaces and that on the orbit spaces of null geodesic congruences in such Lorentzian manifolds. We give the algebra of diffeomorphisms that preserves a null G-structure and demonstrate that in some cases it interpolates between the BMS algebra of an as…
The asymptotic structure of the Pauli-Fierz theory at spatial infinity is investigated in four spacetime dimensions. Boundary conditions on the massless spin-$2$ field that are invariant under an infinite-dimensional group of non-trivial ``improper'' gauge symmetries are given. The compatibility of these boundary conditions with invariance of the theory under Lorentz boosts is a subtle issue which is investigated in depth and leads to the identification of the improper gauge symmetries with the pure BMS supertranslations. It is also shown how rigid Poincaré transformations and improper gauge s…
