Analysis of the Fokker-Planck Equation in Schwarzschild Spacetime: A Supersymmetric Connection

• URL: http://arxiv.org/abs/2506.04643v1
• Date: Thu, 05 Jun 2025 05:24:28 GMT
• Title: Analysis of the Fokker-Planck Equation in Schwarzschild Spacetime: A Supersymmetric Connection
• Authors: Ojaswini Sharma, Aradhya Shukla,
• Abstract summary: We re-analyze the dynamics of the thermal potential within Schwarzschild spacetime by employing the Fokker-Planck equation.<n>We highlight an interesting correspondence between supersymmetric quantum mechanics (SUSY QM) and the Fokker-Planck dynamics associated with the Schwarzschild metric.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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