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In this paper, we show that for one sign of the deformation couplingsingle-trace $T{\bar T}$ deformation moves the holographic screen in G\"{o}deluniverse radially inward. For the other sign of the coupling it moves theholographic screen radially outward. We (thus) argue, on general grounds, thatin holography (single-trace) $T{\bar T}$ deformation can be generally thoughtof as either moving the holographic boundary into the bulk or washing it awayto infinity. In Anti-de Sitter this breaks the spacetime conformal symmetry. Wefurther note that moving timelike holographic boundary into bulk creates acurvature singularity. In the boundary the singularity is understood by stateswith imaginary energies. To make the theory sensible we introduce anultraviolet cutoff and thereby move the boundary into the bulk. In this paperwe first obtain the Penrose limit of the single-trace $T{\bar T}$ deformedstring background and then perform $T$-duality along a space-like isometry toobtain a class of (deformed) G\"{o}del universes. The string background weconsider is $AdS_3\times S^3\times {\cal M}_4$. The single-trace $T{\bar T}$deformation is a particular example of the more general $O(d, d)$transformations.

Moving G\"{o}del's universe holographic screen with $T{\bar T}$