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In this article we probe the proposed holographic duality between $T\bar{T}$deformed two dimensional conformal field theory and the gravity theory of $\rmAdS_3$ with a Dirichlet cutoff by computing correlators of energy-momentumtensor. We focus on the large central charge sector of the $T\bar{T}$ CFT in aEuclidean plane and in a sphere, and compute the correlators of energy-momentumtensor using an operator identity promoted from the classical trace relation.The result agrees with a computation of classical pure gravity in $\rm AdS_3$with the corresponding cutoff surface, given a holographic dictionary whichidentifies gravity parameters with $T\bar{T}$ CFT parameters.

Cutoff $\rm AdS_3$ versus $\rm T\bar{T}$ $\rm CFT_2$ in the large central charge sector: correlators of energy-momentum tensor