Rindler trajectories and Rindler horizons in the Schwarzschild spacetime

We investigate radial linear uniformly accelerated trajectories and their corresponding Rindler horizons in the black hole geometry. In a curved spacetime, a covariant definition for Rindler trajectories is provided in the context of the generalised Letaw-Frenet equations for trajectories with constant curvature scalar and vanishing torsion and hypertorsion. Interestingly, we arrive at a bound on magnitude of acceleration for Rindler trajectories such that, for acceleration greater than the bound value, the Rindler trajectory always falls into the black hole and the distance of closest approach for the trajectory to turn away is always greater than the Schwarzschild radius for all finite boundary data. We further investigate the past and future Rindler horizons using the analytical solution for the trajectories and discuss their features.