Exact analytical solution of the one-dimensional time-dependent radiative transfer equation with linear scattering

•Presents an exact solution to the one-dimensional time-dependent RTE.•Provides a clear view of the transition to the diffusion regime.•Demonstrates the equivalence of the one-dimensional RTE to the Klein-Gordon equation.•Validates the solution using Monte Carlo simulations.•Proposes a method for faster convergence in Monte Carlo sampling.