Holographic Renormalization of Asymptotically Flat Gravity

TL;DR

This paper analyzes the boundary stress tensor in asymptotically flat gravity using Mann-Marolf counterterms, revealing its form across dimensions and confirming its effectiveness for static black hole solutions.

Contribution

It extends the understanding of boundary stress tensors in asymptotically flat spacetimes, especially in higher dimensions, and verifies their conservation and applicability to black hole solutions.

Findings

Boundary stress tensor matches hyperbolic case in 4D

Additional terms in higher dimensions are impotent

Boundary stress tensor conserves and applies to static black holes

Abstract

We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r \rightarrow \infty$, and find that the form of the boundary stress tensor is the same as the hyperbolic boundary case in 4 dimensions, but has additional terms in higher than 4 dimensions. We find that these additional terms are impotent and do not contribute to conserved charges. We also check the conservation of the boundary stress tensor in a sense that $\mathcal{D}^a T_{ab} = 0$, and apply our result to the ($n+3$)-dimensional static black hole solution. As a result, we show that the stress boundary tensor with Mann-Marolf counterterm works well in standard boundary surfaces.