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

Abstract

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.

11 pages, 3 figures; version published in PRD

References in corpus (9)

• The Cosmological Constant and Dark Energy
• The fundamental constants and their variation: observational status and theoretical motivations
• Kaluza-Klein Gravity
• General-Relativistic MHD for the Numerical Construction of Dynamical Spacetimes
• Dynamical Compactification, Standard Cosmology and the Accelerating Universe
• Killing Reduction of 5-Dimensional Spacetimes
• Dynamics of the scalar field in 5-dimensional Kaluza-Klein theory
• Accurate Evaluation of Fermi-Dirac Integrals and Their Derivatives for Arbitrary Degeneracy and Relativity
• 5-Dimensional Kaluza-Klein Theory with a Source