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We derive the geodesic equation for determining the Ryu-Takayanagi surface in$AdS_3$ deformed by single trace $\mu T \bar T + \varepsilon_+ J \bar T +\varepsilon_- T \bar J$ deformation for generic values of $(\mu, \varepsilon_+,\varepsilon_-)$ for which the background is free of singularities. For genericvalues of $\varepsilon_\pm$, Lorentz invariance is broken, and theRyu-Takayanagi surface embeds non-trivially in time as well as spatialcoordinates. We solve the geodesic equation and characterize the UV and IRbehavior of the entanglement entropy and the Casini-Huerta $c$-function. Wecomment on various features of these observables in the $(\mu, \varepsilon_+,\varepsilon_-)$ parameter space. We discuss the matching at leading order insmall $(\mu, \varepsilon_+, \varepsilon_-)$ expansion of the entanglemententropy between the single trace deformed holographic system and a class ofdouble trace deformed theories where a strictly field theoretic analysis ispossible. We also comment on expectation value of a large rectangular Wilsonloop-like observable.

Entanglement Entropy for $T \bar T$, $J \bar T$, $T \bar J$ deformed holographic CFT