  By using simplified 2D gravitational, non-local Lorentz invariant actions
constructed upon the torsion tensor, we discuss the physical meaning of the
remnant symmetries associated with the near-horizon (Milne) geometry
experienced by a radial observer in Schwarzschild spacetime. We then fully
characterize the remnant symmetries corresponding to this near-horizon 2D
geometry by solving the motion equations adapted to 2D Milne space. This
symmetries, which represent special or privileged \emph{diads}, acquire the
form of uniformly accelerated (Rindler) observers whose constant acceleration
is proportional to the black hole mass $M$.
