Photon diffusion in a relativistically expanding sphere

A relativistically expanding sphere exists in many explosive astrophysical systems, including gamma-ray bursts, neutron star mergers, and some supernovae. In this paper we investigate the photon diffusion process in a relativistically expanding sphere, which is important for understanding the energetic and radiative characters of the above mentioned explosive systems. The following contents are discussed in the frame work of special relativity: random walks of photons by scattering with electrons, photospheres, photon diffusion, and the energy flux density emerging from the surface of the expanding sphere. Some of the results are also applicable to the Universe since the Universe is also a spherical expanding system.