Role of the remnant symmetries in gravitational theories based on absolute parallelism: a 2D standpoint

TL;DR

This paper investigates the remnant symmetries in 2D gravitational models based on torsion, revealing their connection to near-horizon geometries and accelerated observers in Schwarzschild spacetime.

Contribution

It characterizes the remnant symmetries in 2D torsion-based gravity models and links them to near-horizon geometries and observer acceleration.

Findings

Remnant symmetries correspond to privileged diads in 2D Milne space.

Symmetries resemble uniformly accelerated Rindler observers.

Acceleration is proportional to black hole mass M.

Abstract

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 $M$.