  We consider gravitational perturbations of 2D dilaton gravity systems and
show that these can be recast into $T\bar{T}$-deformations (at least) under
certain conditions, where $T$ means the energy-momentum tensor of the matter
field coupled to a dilaton gravity. In particular, the class of theories under
this condition includes a Jackiw-Teitelboim (JT) theory with a negative
cosmological constant including conformal matter fields. This is a
generalization of the preceding work on the flat-space JT gravity by S.
Dubovsky, V. Gorbenko and M. Mirbabayi [arXiv:1706.06604].
