2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/201902We consider $d>4$-dimensional space-times which are asymptotically flat at spatial infinity and show that, in the first order framework, the action principle is well-defined \emph{without the need of infinite counter terms.} It naturally leads to a covariant phase space in which the Hamiltonians generating asymptotic symmetries provide the total energy-momentum and angular momentum of the isolated system. This work runs parallel to our previous analysis in four dimensions \cite{aes}. The higher dimensional analysis is in fact simpler because of absence of logarithmic and super translation ambiguities.12 pages, no figures. Extends the 4 dimensional analysis of arXiv:0802.2527 to higher dimensionsGeneral Relativity and Quantum Cosmologytext