Energy Decay in $1+1$ Rindler Spacetime

TL;DR

This paper proves polynomial decay of scalar wave energy in 1+1 Rindler spacetime, using vector field methods similar to those in Schwarzschild and Minkowski spacetimes, enhancing understanding of wave behavior near horizons.

Contribution

It demonstrates polynomial energy decay for solutions of the wave equation in 1+1 Rindler spacetime using adapted vector field techniques.

Findings

Polynomial decay of energy flux near null infinity.

Decay estimates near the Rindler horizon.

Application of vector field method in Rindler spacetime.

Abstract

We consider solutions of the massless scalar wave equation $\Box_g\psi=0$ 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.