General solutions in Chern-Simons gravity and $T \bar T$-deformations

Understand

We find the most general solution to Chern-Simons AdS$_3$ gravity in Fefferman-Graham gauge.

• The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection.
• We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism.
• Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $T \bar T$-deformation.