Counterterms in Massive Gravity Theory

Abstract

We derived local boundary counterterms in massive gravity theory with a negative cosmological constant in four dimensions. With these counterterms at hand we analyzed the properties of the boundary field theory in the context of AdS/CFT duality by calculating the boundary stress energy tensor. The calculation shows that the boundary stress energy tensor is conserved, and momentum dissipation might occur on the level of linear response only. We also calculated the thermodynamic quantities and the boundary stress energy tensor for a specific type of solutions. The thermodynamic potentials agree with the results of literature up to some constants which can be removed by adding finite counterterms.

revtex4, 13pages, no figure. The form of the counterterms slightly changed and some formulae corrected. 2 citations added. Language slightly modified

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• On dRGT massive gravity with degenerate reference metrics
• Emergent Universe Scenario, Bouncing and Cyclic Universes in Degenerate Massive Gravity
• The holographic p+ip solution failed to win the competition in dRGT massive gravity
• Holography without counter terms
• Static spheres and Aschenbach effect for black holes in massive gravity
• Hamilton-Jacobi Approach to Holographic Renormalization of Massive Gravity
• The equivalence between Finsler and non-commutative geometries by massive gravity black hole
• Holographic Complexity Growth Rate in a dual FLRW Universe
• Holographic renormalization by Hamilton-Jacobi formulation with generated ansatz
• Topological charge and black hole photon spheres in massive gravity