The extended BMS group includes supertranslation, dual supertranslation and Lorentz transformations. The generators of these symmetries can be classified according to their parity into "electric" and "magnetic" types. Using a multipole expansion of gravitational sources in the Newman-Penrose formalism, we associate each one of these charges with a particular moment. At leading order, the "electric" and "magnetic" monopole moments correspond respectively to supertranslations and dual supertranslations. At the first subleading order, the "electric" and "magnetic" dipole moments correspond respectively to boosts and rotations, therefore comprising the entire Lorentz group. Electric-magnetic type of duality then rotates the boost and rotation generators into each other.
We supplement the recently found dual gravitational charges with dual charges for the whole BMS symmetry algebra. Furthermore, we extend the dual charges away from null infinity, defining subleading dual charges. These subleading dual charges complement the subleading BMS charges in the literature and together account for all the Newman-Penrose charges.
In this paper we establish a relation between the non-linearly conserved Newman-Penrose charges and certain subleading terms in a large-$r$ expansion of the BMS charges in an asymptotically-flat spacetime. We define the subleading BMS charges by considering a $1/r$-expansion of the Barnich-Brandt prescription for defining asymptotic charges in an asymptotically-flat spacetime. At the leading order, i.e. $1/r^0$, one obtains the standard BMS charges, which would be integrable and conserved in the absence of a flux term at null infinity, corresponding to gravitational radiation, or Bondi news. A…
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.
In this paper we study the BMS symmetry of the celestial OPE of two positive helicity gravitons in Einstein theory in four dimensions. The celestial OPE is obtained by Mellin transforming the scattering amplitude in the (holomorphic) collinear limit. The collinear limit at leading order gives the singular term of the celestial OPE. We compute the first subleading correction to the OPE by analysing the four graviton scattering amplitude directly in Mellin space. The subleading term can be written as a linear combination of BMS descendants with the OPE coefficients determined by BMS algebra and …
The relationships between extended BMS symmetries at null infinity and Weinberg's soft theorems for gravitons and photons together with their subleading generalizations are developed using ambitwistor string theory. Ambitwistor space is the phase space of complex null geodesics in complexified space-time. We show how it can be canonically identified with the cotangent bundle of null infinity. BMS symmetries of null infinity lift to give a hamiltonian action on ambitwistor space, both in general dimension and in its twistorial 4-dimensional representation. General vertex operators arise from ha…
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.
Due to seminal works of Weinberg, Cachazo and Strominger we know that tree level quantum gravity amplitudes satisfy three factorization constraints. Building on previous works which relate two of these constraints to symmetries of quantum gravity at null infinity, we present rather strong evidence that the third constraint is also equivalent to a new set of symmetries of (perturbative) quantum gravity. Our analysis implies that the symmetry group of quantum gravity may be even richer than the BMS group (or infinite dimensional extension thereof) previously considered.
We derive a closed-form expression of the orbit of Minkowski spacetime under arbitrary Diff$(S^2)$ super-Lorentz transformations and supertranslations. Such vacua are labelled by the superboost, superrotation and supertranslation fields. Impulsive transitions among vacua are related to the refraction memory effect and the displacement memory effect. A phase space is defined whose asymptotic symmetry group consists of arbitrary Diff$(S^2)$ super-Lorentz transformations and supertranslations. It requires a renormalization of the symplectic structure. We show that our final surface charge express…
We apply the new method based on null geodesics for detecting gravitational memory and find the bulk memory in Newman-Unti gauge around the boundary of the conformally compactified space time. We show how we use the newly found conserved charges in the subleading orders of large-$r$ expansion of the BMS charges to define the gravitational memory at each order in the non-linearised gravitational theory. We also find the gravitational shift in the $r$ direction. It is shown that the longitudinal displacement at order $1/r$ is the relative radius change between two detectors derived by Strominger…
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…
The surface charge algebra of generic asymptotically locally (A)dS$_4$ spacetimes without matter is derived without assuming any boundary conditions. Surface charges associated with Weyl rescalings are vanishing while the boundary diffeomorphism charge algebra is non-trivially represented without central extension. The $Λ$-BMS$_4$ charge algebra is obtained after specifying a boundary foliation and a boundary measure. The existence of the flat limit requires the addition of corner terms in the action and symplectic structure that are defined from the boundary foliation and measure. The flat li…
This is a review of selected topics from recent work on symmetry charges in asymptotically flat spacetime done by the author in collaboration with U. Kol and R. Javadinezhad. First we reinterpret the reality constraint on the boundary graviton as the gauge fixing of a new local symmetry, called dual supertranslations. This symmetry extends the BMS group and bears many similarities to the dual (magnetic) gauge symmetry of electrodynamics. We use this new gauge symmetry to propose a new description of the TAUB-NUT space that does not contain closed time-like curves. Next we summarize progress to…
We show that the asymptotic charges associated with Lorentz symmetries on past and future null infinity match in the limit to spatial infinity in a class of asymptotically-flat spacetimes. These are spacetimes that obey the Ashtekar-Hansen definition of asymptotic flatness at null and spatial infinity and satisfy an additional set of conditions which we lay out explicitly. Combined with earlier results on the matching of supertranslation charges, this shows that all Bondi-Metzner-Sachs (BMS) charges on past and future null infinity match in the limit to spatial infinity in this class of spacet…
We present an explicit formula for Lorentz boosts and rotations that commute with BMS supertranslations in asymptotically flat spacetimes. Key to the construction is the use of infrared regularizations and of a unitary transformation that makes observables commute with the soft degrees of freedom. We explicitly verify that our charges satisfy the Lorentz algebra and we check that they are consistent with expectations by evaluating them on the supertranslated Minkowski space and on the boosted Kerr black hole.
The most general vacuum solution to Einstein's field equations with no incoming radiation can be constructed perturbatively from two infinite sets of canonical multipole moments, which are found to be mapped into each other under gravitational electric-magnetic duality at the non-linear level. We demonstrate that in non-radiative regions such spacetimes are completely characterized by a set of conserved celestial charges that consist of the Geroch-Hansen multipole moments, the generalized BMS charges and additional celestial multipoles accounting for subleading memory effects. Transitions amon…
We extend the BMS(4) group by adding logarithmic supertranslations. This is done by relaxing the boundary conditions on the metric and its conjugate momentum at spatial infinity in order to allow logarithmic terms of carefully designed form in the asymptotic expansion, while still preserving finiteness of the action. Standard theorems of the Hamiltonian formalism are used to derive the (finite) generators of the logarithmic supertranslations. As the ordinary supertranslations, these depend on a function of the angles. Ordinary and logarithmic supertranslations are then shown to form an abelian…
