Abstract
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 BM S4 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 BM S4 algebra with the angle dependent u(1) transformations. The Hamiltonian charge-generator associated with each asymptotic symmetry element is explicitly written. The connection with matching conditions at null infinity is also discussed.
Highlights
By contrast, the description of the dynamics on Cauchy hypersurfaces is Hamiltonian even if there is gravitational radiation, since Cauchy hypersurfaces capture the whole dynamical system
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 BM S4 algebra, and leads to a non-divergent behaviour of the Weyl tensor as one approaches null infinity
We extend the analysis to the coupled Einstein-Maxwell system and obtain as canonically realized asymptotic symmetry algebra a semi-direct sum of the BM S4 algebra with the angle dependent u(1) transformations
Summary
Our boundary conditions strongly rely on the approach developed in [15], where parity conditions were imposed on the leading orders of the asymptotic fields. As in the gravitational case, while imposing these twisted parity conditions leads to a well-defined system, this choice excludes magnetic monopoles and introduces solutions possessing a logarithmic divergent electromagnetic field at null infinity It was shown in [14] that it is sufficient for this twist to be an improper gauge transformation (for “improper”, we follow the terminology of [16]). This leads to the introduction of a set of hybrid parity conditions combining the best of both choices: a non-trivial action of the enhanced asymptotic symmetry algebra, the absence of solutions diverging at null infinity and the possibility to describe magnetic monopoles. No such additional degree of freedom is necessary in the case of gravity
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