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 $\mathcal{C}$ with the past null infinity ${\mathcal{J}}^{-}$ and future null infinity ${\mathcal{J}}^{+}$ 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 $|a|\le |a{|}_b$ found earlier [K. Paithankar and S. Kolekar, Phys. Rev. D 99, 064012 (2019)].

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• Classical black holes
• General relativity