Boundary Terms for Massive General Relativity

Abstract

It is well-known that the presence of a spacetime boundary requires the conventional Einstein-Hilbert (EH) action to be supplemented by the Gibbons-Hawking (GH) boundary term in order to retain the standard variational procedure. When the EH action is amended by the diffeomorphism-invariant graviton mass and potential terms, it naively appears that no further boundary terms are needed since all the new fields of massive gravity enter the action with the first derivative. However, we show that such a formulation would be inconsistent, even when the bulk action is ghost-free. The theory is well-defined only after introducing novel boundary counterterms, which dominate over the GH term in the massless limit and cancel the problematic boundary terms induced by the bulk action. The number of boundary counterterms equals the number of total derivatives one could construct in the bulk using positive powers of two derivatives of the longitudinal mode of the massive graviton.

arXiv comment25 pages, 1 figure; version published in PRD

References in corpus (11)

• 4D Gravity on a Brane in 5D Minkowski Space
• Resummation of Massive Gravity
• The Einstein Equations on the 3-Brane World
• Generalization of the Fierz-Pauli Action
• Brane cosmological evolution in a bulk with cosmological constant
• Bimetric Gravity from Ghost-free Massive Gravity
• Effective Field Theory for Massive Gravitons and Gravity in Theory Space
• Strong Interactions and Stability in the DGP Model
• Ghost-free Massive Gravity with a General Reference Metric
• A Proof Of Ghost Freedom In de Rham-Gabadadze-Tolley Massive Gravity
• A Scale-up of Lambda_3

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