The Finiteness Requirement for Six-Dimensional Euclidean Einstein Gravity
G.W.Gibbons, S.Ichinose
TL;DR
This paper demonstrates that in six-dimensional Euclidean Einstein gravity, the strict finiteness condition restricts solutions to only flat metrics, based on analysis of counterterms in Ricci-flat manifolds.
Contribution
It establishes the finiteness requirement as a strong constraint, showing only flat metrics satisfy it in 6D Euclidean Einstein gravity, extending previous understanding from 4D.
Findings
Finiteness condition restricts solutions to flat metrics in 6D
Counterterms analyzed in Ricci-flat manifolds support the result
Finiteness requirement is more stringent than previously thought
Abstract
The finiteness requirement for Euclidean Einstein gravity is shown to be so stringent that only the flat metric is allowed. We examine counterterms in 4D and 6D Ricci-flat manifolds from general invariance arguments.
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