Holographic Renormalization of Asymptotically Flat Gravity

Abstract

We compute the boundary stress tensor associated with Mann-Marolf counterterm in asymptotic flat and static spacetime for cylindrical boundary surface as $r\to \infty$, 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.

27 pages

References in corpus (1)

• On the Stress Tensor for Asymptotically Flat Gravity

Cited by in corpus (4)

• The BMS4 algebra at spatial infinity
• Asymptotic Renormalization in Flat Space: Symplectic Potential and Charges of Electromagnetism
• Aspects of the zero $\Lambda$ limit in the AdS/CFT correspondence
• Deformations of Lifshitz holography with the Gauss-Bonnet term in ($n+1$) dimensions