Generalised geometry from the ground up

Extending previous work on generalised geometry, we explicitly construct an E7-valued vielbein in eleven dimensions that encompasses the scalar bosonic degrees of freedom of D=11 supergravity, by identifying new "generalised vielbeine" in eleven dimensions associated with the dual 6-form potential and the dual graviton. By maintaining full on-shell equivalence with the original theory at every step, our construction altogether avoids the constraints usually encountered in other approaches to generalised geometry and, as a side product, also furnishes the non-linear ansatz for the dual (magnetic) 7-form flux for any non-trivial compactification of D=11 supergravity, complementing the known non-linear ansaetze for the metric and the 4-form flux. A preliminary analysis of the generalised vielbein postulate for the new vielbein components reveals tantalising hints of new structures beyond D=11 supergravity and ordinary space-time covariance, and also points to the possible D=11 origins of the embedding tensor. We discuss the extension of these results to E8

BMS charges in polyhomogeneous spacetimes

We classify the asymptotic charges of a class of polyhomogeneous asymptotically-flat spacetimes with finite shear, generalising recent results on smooth asymptotically-flat spacetimes. Polyhomogenous spacetimes are a formally consistent class of spacetimes that do not satisfy the well-known peeling property. As such, they constitute a more physical class of asymptotically-flat spacetimes compared to the smooth class. In particular, we establish that the generalised conserved non-linear Newman-Penrose charges that are known to exist for such spacetimes are a subset of asymptotic BMS charges.Comment: 42 page

Asymptotic Gravitational Charges

We present a method for finding, in principle, all asymptotic gravitational charges. The basic idea is that one must consider all possible contributions to the action that do not affect the equations of motion for the theory of interest; such terms include topological terms. As a result we observe that the first order formalism is best suited to an analysis of asymptotic charges. In particular, this method can be used to provide a Hamiltonian derivation of recently found dual charges.Comment: 5 page

Hamiltonian derivation of dual gravitational charges

Abstract We provide a Hamiltonian derivation of recently discovered dual BMS charges. In order to do so, we work in the first order formalism and add to the usual Palatini action, the Holst term, which does not contribute to the equations of motion. We give a method for finding the leading order integrable dual charges à la Wald-Zoupas and construct the corresponding charge algebra. We argue that in the presence of fermions, the relevant term that leads to dual charges is the topological Nieh-Yan term.</jats:p

Uniqueness of the Kerr–de Sitter Spacetime as an Algebraically Special Solution in Five Dimensions

We determine the most general solution of the five-dimensional vacuum Einstein equation, allowing for a cosmological constant, with (i) a Weyl tensor that is type II or more special in the classification of Coley et al., (ii) a non-degenerate "optical matrix" encoding the expansion, rotation and shear of the aligned null direction. The solution is specified by three parameters. It is locally isometric to the 5d Kerr-de Sitter solution, or related to this solution by analytic continuation or taking a limit. This is in contrast with four dimensions, where there exist infinitely many solutions with properties (i) and (ii).This work was supported by the European Research Council grant no. ERC-2011-StG 279363-HiDGR. G.B.F. is supported by CAPES grant no. 0252/11-5. M.G. is supported by King’s College, Cambridge.This is the final version of the article. It first appeared from Springer via http://dx.doi.org/10.1007/s00220-015-2447-

Higher derivative asymptotic charges and internal Lorentz symmetries

In line with a recent proposal for the study of asymptotic gravitational charges, we investigate higher derivative asymptotic charges. We show that the higher derivative BMS charges are related to the two-derivative BMS charges. Significantly, we find that internal Lorentz transformations are relevant in the higher derivative case in contrast to the two-derivative case. We give a prescription for their precise definition and derive the associated charges, finding, again, a relation with two-derivative BMS charges.Comment: 20 page

Weyl Double Copy for Gravitational Waves

We establish the status of the Weyl double copy relation for radiative solutions of the vacuum Einstein equations. We show that all type N vacuum solutions, which describe the radiation region of isolated gravitational systems with appropriate falloff for the matter fields, admit a degenerate Maxwell field that squares to give the Weyl tensor. The converse statement also holds, i.e., if there exists a degenerate Maxwell field on a curved background, then the background is type N . This relation defines a scalar that satisfies the wave equation on the background. We show that for nontwisting radiative solutions, the Maxwell field and the scalar also satisfy the Maxwell equation and the wave equation on Minkowski spacetime. Hence, nontwisting solutions have a straightforward double copy interpretation