Axion electrodynamics and magnetohydrodynamics

Maxwell equations in curved spacetime

“…In realistic astrophysical situations, Maxwell's equations should be dynamically combined with Einstein's equation with accompanying fluids and other fields. The complete sets of Einstein's equation with a fluid and a scalar field (with additional helical coupling with the EM fields) in the covariant, the ADM, and the FNLE formulations are presented in [9]. Maxwell's equations in the general curved spacetime derived in different forms in this work are applicable in all these situations.…”

“…φ is a scalar field with f = φ for the conventional axion coupling [8]. A system together with Einstein's gravity, scalar field, and a general fluid is studied in [9].…”

“…Maxwell's equations in the ADM formulation are presented in textbooks of numerical relativity [11][12][13]; see Eqs. (65)-(73) in [9]. Equations can be arranged, including the axion coupling, as…”

“…where ∇ i is an ordinary derivative associated with δ i j . Useful relations needed for the derivation can be found in [9]. In terms of the effective polarization and magnetization vectors, these can be arranged as…”

Axion cosmology with post-Newtonian corrections

“…This approximation is relevant in many astrophysical situations including cosmology; in observable universe, except for nearby compact objects like neutron stars and black holes, the gravity represented by a dimensionless metric parameter Φ/c 2 is extremely small with typical value less than 10 −5 [12]. The weak gravity limit of a general scalar field (including axion) in cosmology is presented in [13] in the context of electrodynamics and magnetohydrodynamics.…”