Infinite towers of supertranslation and superrotation memories

A framework that structures the gravitational memory effects and which is consistent with gravitational electric-magnetic duality is presented. A correspondence is described between memory observables, particular subleading residual gauge transformations, associated overleading gauge transformations and their canonical surface charges. It is shown that matter-induced transitions can generate infinite towers of independent memory effects at null infinity. These memories are associated with an infinite number of conservation laws at spatial infinity which lead to degenerate towers of subleading soft graviton theorems. It is shown that the leading order mutually commuting supertranslations and (novel) superrotations are both associated with a leading displacement memory effect, which suggests the existence of new boundary conditions.Comment: 5 pages. Proof of existence of towers of memories added. To be published in PR

Bulk supertranslation memories: a concept reshaping the vacua and black holes of general relativity

The memory effect is a prediction of general relativity on the same footing as the existence of gravitational waves. The memory effect is understood at future null infinity as a transition induced by null radiation from a Poincar\'e vacuum to another vacuum. Those are related by a supertranslation, which is a fundamental symmetry of asymptotically flat spacetimes. In this essay, I argue that finite supertranslation diffeomorphisms should be extended into the bulk spacetime consistently with canonical charge conservation. It then leads to fascinating geometrical features of gravitational Poincar\'e vacua. I then argue that in the process of black hole merger or gravitational collapse, dramatic but computable memory effects occur. They lead to a final stationary metric which qualitatively deviates from the Schwarzschild metric.Comment: 5 pages + bibliography. Honorable mention at the Gravity Research Foundation 2016 Essay Contes

Semi-classical central charge in topologically massive gravity

It is shown that the warped black holes geometries discussed recently in 0807.3040 admit an algebra of asymptotic symmetries isomorphic to the semi-direct product of a Virasoro algebra and an algebra of currents. The realization of this asymptotic symmetry by canonical charges allows one to find the central charge of the Virasoro algebra. The right-moving central charge $c_R = \frac{(5\hat{\nu}^2+3)l}{G\hat{\nu} (\hat{\nu}^2+3)}$ is obtained when the Virasoro generators are normalized in order to have a positive zero mode spectrum for the warped black holes. The current algebra is also shown to be centrally-extended.Comment: major sign mistake in the central charge corrected. Conclusion adapted. Minor typos correcte

Vacua of the gravitational field

The Poincar\'e invariant vacuum is not unique in quantum gravity. The BMS supertranslation symmetry originally defined at null infinity is spontaneously broken and results in inequivalent Poincar\'e vacua. In this paper we construct the unique vacua which interpolate between past and future null infinity in BMS gauge and which are entirely characterized by an arbitary Goldstone boson defined on the sphere which breaks BMS invariance. We show that these vacua contain a defect which carries no Poincar\'e charges but which generically carries superrotation charges. We argue that there is a huge degeneracy of vacua with multiple defects. We also present the single defect vacua with its canonically conjugated source which can be constructed from a Liouville boson on the stereographic plane. We show that positivity of the energy forces the stress-tensor of the boson to vanish as a boundary condition. Finite superrotations, which turn on the sources, are therefore physically ruled out as canonical transformations around the vacua. Yet, infinitesimal superrotations are external symplectic symmetries which are associated with conserved charges which characterize the Goldstone boson.Comment: Accepted in JHEP, comments added, 34 page

Asymptotically flat spacetimes with BMS3_3 symmetry

We construct the phase space of 3-dimensional asymptotically flat spacetimes that forms the bulk metric representation of the BMS group consisting of both supertranslations and superrotations. The asymptotic symmetry group is a unique copy of the BMS group at both null infinities and spatial infinity. The BMS phase space obeys a notion of holographic causality and can be parametrized by boundary null fields. This automatically leads to the antipodal identification of bulk fields between past and future null infinity in the absence of a global conical defect.Comment: 22 page

Classical static final state of collapse with supertranslation memory

The Kerr metric models the final classical black hole state after gravitational collapse of matter and radiation. Any stationary metric which is close to the Kerr metric has been proven to be diffeomorphic to it. Now, finite supertranslation diffeomorphisms are symmetries which map solutions to inequivalent solutions as such diffeomorphisms generate conserved superrotation charges. The final state of gravitational collapse is therefore parameterized by its mass, angular momentum and supertranslation field, signaled by its conserved superrotation charges. In this paper, we first derive the angle-dependent energy conservation law relating the asymptotic value of the supertranslation field of the final state to the details of the collapse and subsequent evolution of the system. We then generate the static solution with an asymptotic supertranslation field and we study some of its properties. Up to a caveat, the deviation from the Schwarzschild metric could therefore be predicted on a case-by-case basis from accurate modeling of the angular dependence of the ingoing and outgoing energy fluxes leading to the final state.Comment: 35 pages, 7 figures, published version (only refs updated with respect to v2

The Λ\Lambda-BMS4_4 group of dS4_4 and new boundary conditions for AdS4_4

Using the dictionary between Bondi and Fefferman-Graham gauges, we identify the analogues of the Bondi news, Bondi mass and Bondi angular momentum aspects at the boundary of generic asymptotically locally (A)dS$_4$ spacetimes. We introduce the $\Lambda$-BMS$_4$ group as the residual symmetry group of the metric in Bondi gauge after boundary gauge fixing. This group consists of infinite-dimensional non-abelian supertranslations and superrotations and it reduces in the asymptotically flat limit to the extended BMS$_4$ group. Furthermore, we present new boundary conditions for asymptotically locally AdS$_4$ spacetimes which admit $\mathbb R$ times the group of area-preserving diffeomorphisms as the asymptotic symmetry group. The boundary conditions amount to fix 2 components of the holographic stress-tensor while allowing 2 components of the boundary metric to fluctuate. They correspond to a deformation of a holographic CFT$_3$ which is coupled to a fluctuating spatial metric of fixed area.Comment: 42 pages, 1 figure, attached Mathematica notebook, published versio

On Asymptotic Flatness and Lorentz Charges

In this paper we establish two results concerning four-dimensional asymptotically flat spacetimes at spatial infinity. First, we show that the six conserved Lorentz charges are encoded in two unique, distinct, but mutually dual symmetric divergence free tensors that we construct from the equations of motion. Second, we show that integrability of Einstein's equations in the asymptotic expansion is sufficient to establish the equivalence between counter-term charges defined from the variational principle and charges defined by Ashtekar and Hansen. These results clarify earlier constructions of conserved charges in the hyperboloid representation of spatial infinity. In showing this, parity condition on the mass aspect is not needed. Along the way in establishing these results, we prove two lemmae on tensor fields on three dimensional de Sitter spacetime stated by Ashtekar-Hansen and Beig-Schmidt and state and prove three additional lemmae.Comment: 26 pages; no figures; v2: minor changes; v3: clarifications + references + a new lemma added, results unaffecte