Fokker–Planck equation in Schwarzschild spacetime: A supersymmetric connection

We have re-analyzed the dynamics of the thermal potential within Schwarzschild spacetime by employing the Fokker–Planck equation. We demonstrate that the Fokker–Planck equation reduces to a simplified form equivalent to a scaled quantum mechanical problem with a harmonic oscillator potential. In this framework, we highlight an interesting correspondence between supersymmetric quantum mechanics (SUSY QM) and the Fokker–Planck dynamics associated with the Schwarzschild metric. Utilizing the isospectral deformation, an intrinsic feature of SUSY QM, we derive a family of one-parameter isospectral potentials. Notably, this new class of potentials exhibits the same energy spectrum as the original harmonic oscillator potential, but with distinct wavefunctions.