Effects of Spatial Curvature on Blackbody Radiation: An Analog Model for Modified Radiation Laws

Abstract

In this paper, we investigate the effects of spatial curvature on blackbody radiation using an analog model based on a quantum harmonic oscillator on a circle. Through a gnomonic projection, the curved oscillator is mapped onto a straight-line coordinate representation, while the effects of curvature are retained in the modified energy spectrum. Using this curvature-dependent spectrum, we derive generalized forms of the Planck, Stefan–Boltzmann, Rayleigh–Jeans, and Wien laws. Our results show that increasing the curvature parameter reduces both the height and width of the Planck spectrum and shifts its peak toward lower frequencies. We also find that the Stefan–Boltzmann law acquires a curvature-dependent correction that reduces the radiative flux at a fixed temperature. We further analyze the influence of spatial curvature on the Rayleigh–Jeans and Wien laws and recover the generalized Rayleigh–Jeans limit in the appropriate long-wavelength regime. These results demonstrate how spatial curvature can modify the thermal properties of radiation within the proposed analog model.