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We consider critical gravity as van Dam-Vletman-Zakharov (vDVZ) discontinuityin anti de Sitter space. For this purpose, we introduce the higher curvaturegravity. This discontinuity can be confirmed by calculating the residues ofrelevant poles explicitly. For the non-critical gravity of$0<m_2^2<-2\Lambda/3$, the scalar residue of a massive pole is given by 2/3when taking the $\Lambda \to 0$ limit first and then the $m^2_2 \to 0$ limit.This indicates that the vDVZ discontinuity occurs in the higher curvaturetheory, showing that propagating degrees of freedom is decreased from 5 to 3.However, at the critical point of $m^2_2=-2\Lambda/3$, the tensor residue of amassive pole blows up and scalar residue is -5/36, showing the unpromisingfeature of the critical gravity.

Critical gravity as van Dam-Veltman-Zakharov discontinuity in anti de Sitter space