Action and Hamiltonians in higher dimensional general relativity: First order framework

TL;DR

This paper demonstrates that in higher-dimensional (d>4) asymptotically flat spacetimes, the first order action principle is well-defined without counter terms, enabling a covariant phase space formulation for conserved quantities.

Contribution

It extends the first order framework for asymptotically flat spacetimes to higher dimensions, simplifying the analysis by avoiding certain ambiguities present in four dimensions.

Findings

Action principle is well-defined without infinite counter terms.

Hamiltonians generate asymptotic symmetries and define conserved quantities.

Higher dimensions lack logarithmic and super translation ambiguities.

Abstract

We 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.