Asymptotically flat space-times in tetrad-connection form.

What is it about?

We examine asymptotically flat space-times (i.e. those that approach Minkowski space at large hyperbolic radius). In particular we examine these in the context of first-order (tetra-connection) gravity, written in the Palatini action. In this paper we derive finiteness of the action, symplectic structure, and the conserved quantities corresponding to energy, momentum and angular momentum.

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Why is it important?

In the second order (normal) way of examining things, an infinite subtraction must be performed to render the theory finite. This seems rather ad-hoc, as it relies on embedding a space-time in Minkowski space and subtracting its extrinsic curvature. However, this embedding isn't always possible. By looking at things in terms of tetrads and connections, we find that there is no need for this subtraction, everything is naturally finite, and we do not need to rely on any external structure.