State-Relevant Maxwell's Equation from Kaluza-Klein Theory

We study a five-dimensional perfect fluid coupled with Kaluza-Klein (KK) gravity. By dimensional reduction, a modified form of Maxwell's equation is obtained, which is relevant to the equation of state of the source. Since the relativistic magnetohydrodynamics (MHD) and the 3-dimensional formulation are widely used to study space matter, we derive the modified Maxwell's equations and relativistic MHD in 3+1 form. We then take an ideal Fermi gas as an example to study the modified effect, which can be visible under high density or high energy condition, while the traditional Maxwell's equation can be regarded as a result in the low density and low temperature limit. We also indicate the possibility to test the state-relevant effect of KK theory in a telluric laboratory.