Energy Decay in $1+1$ Rindler Spacetime

We consider solutions of the massless scalar wave equation ${\mathrm{\square }}_g\psi =0$ on a fixed Rindler background and show polynomial decay of the energy flux related to the Rindler observers near null infinity and to local observers near the Rindler horizon. The main estimates are obtained via the vector field method using suitable vector fields multipliers which are analogous to the ones used in Schwarzschild spacetime and Minkowski spacetime.