Rindler horizons in a Schwarzschild spacetime

We investigate the past and future Rindler horizons for radial Rindler trajectories in a Schwarzschild spacetime. We assume the Rindler trajectory to be linearly uniformly accelerated (LUA) throughout its motion, in the sense of the curved spacetime generalization of the Letaw-Frenet equations. The analytical solution for the radial LUA trajectories along with its past and future intercepts C with the past null infinity J− and future null infinity J+ are presented. The Rindler horizons in the presence of the black hole are found to depend on both the magnitude of acceleration |a| and the asymptotic initial data h, unlike in the flat Rindler spacetime case, wherein they are only a function of the global translational shift h. The horizon features are discussed. The Rindler quadrant structure provides an alternate perspective to interpret the acceleration bounds |a|≤|a|b found earlier [K. Paithankar and S. Kolekar, Phys. Rev. D 99, 064012 (2019)].