Supertranslations and Holographic Stress Tensor

TL;DR

This paper explores how different supertranslation choices affect the boundary stress tensor in asymptotically flat spacetimes, showing that the covariant phase space remains well-defined regardless of these choices.

Contribution

It demonstrates that all supertranslation frames are permissible and that the boundary stress tensor's leading order is unaffected by these choices, while the next order depends on the frame.

Findings

Covariant phase space is well-defined for all supertranslation choices.

Leading order boundary stress tensor is insensitive to supertranslation frames.

Next order boundary stress tensor transforms consistently with special relativity.

Abstract

It is well known in the context of four dimensional asymptotically flat spacetimes that the leading order boundary metric must be conformal to unit de Sitter metric when hyperbolic cutoffs are used. This situation is very different from asymptotically AdS settings where one is allowed to choose an arbitrary boundary metric. The closest one can come to changing the boundary metric in the asymptotically flat context, while maintaining the group of asymptotic symmetries to be Poincare, is to change the so-called `supertranslation frame' \omega. The most studied choice corresponds to taking \omega = 0. In this paper we study consequences of making alternative choices. We perform this analysis in the covariant phase space approach as well as in the holographic renormalization approach. We show that all choices for \omega are allowed in the sense that the covariant phase space is well defined irrespective of how we choose to fix supertranslations. The on-shell action and the leading order boundary stress tensor are insensitive to the supertranslation frame. The next to leading order boundary stress tensor depends on the supertranslation frame but only in a way that the transformation of angular momentum under translations continues to hold as in special relativity.