Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis

TL;DR

$In five spacetime dimensions, the paper develops a Hamiltonian treatment of gravity at spatial infinity and uncovers an infinite-dimensional asymptotic symmetry, the group denoted $BMS_5$, which includes a four-function family of angle-dependent leading and subleading supertranslations. $Through careful boundary conditions, the authors construct finite canonical generators and compute the full (non-linear) BMS_5 algebra, including central charges and field-dependent nonlinearities; they show that a linear realization of the Lorentz subalgebra is possible, though some nonlinearities in boosts with leading supertranslations persist. $A nonlinear, advantageous reformulation is then presented: an Abelian description of the leading supertranslations with a central extension, together with a linear Lorentz sector, realized via specific nonlinear redefinitions of generators, and the energy is shown to transform with essential nonlinear contributions that guarantee supertranslation invariance. $The work also discusses energy positivity/transform properties, the matching with null infinity, and potential generalizations to higher dimensions, highlighting open questions about the interpretation of the enlarged supertranslation sector and the inclusion of superrotations.$

Abstract

We develop the analysis of the asymptotic properties of gravity in higher spacetime dimensions $D$, with a particular emphasis on the case $D=5$. Our approach deals with spatial infinity and is Hamiltonian throughout. It is shown that the asymptotic symmetry algebra BMS$_5$, which is realized non linearly, contains a four-fold family of angle-dependent supertranslations. The structure of this non-linear algebra is investigated and a presentation in which the Poincaré subalgebra is linearly realized is constructed. Invariance of the energy is studied. Concluding comments on higher dimensions $D \geq 6$ are also given.