Rindler horizons in a Schwarzschild spacetime

Abstract

We investigate the past and future Rindler horizons for radial Rindler trajectories in the Schwarzschild spacetime. We assume the Rindler trajectory to be linearly uniformly accelerated (LUA) throughout its motion, in the sense of the curved spacetime generalisation of the Letaw-Frenet equations. The analytical solution for the radial LUA trajectories along with its past and future intercepts ${\cal C}$ with the past null infinity ${\cal J^-}$ and future null infinity ${\cal J^+}$ 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, $|a| \leq |a|_b$ found earlier in arXiv:1901.04674.