Maxwell-dilaton dynamics

Abstract

The dynamics of Maxwell-dilaton theory in Minkowski spacetime are studied using fully nonlinear, numerical evolutions. This model represents the flat-space sector of Einstein-Maxwell-Dilaton theory which has attracted interest recently because it is a well-posed alternative to general relativity, and it also represents the abelian sector of Yang-Mills-Dilaton. As such, understanding its dynamics may shed light on the dynamics of the respective larger systems. In particular, we study electric, magnetic, and dyonic monopoles as well as the flux tubes studied previously by Gibbons and Wells. Some scenarios produce large gradients that an increasing adaptive mesh refinement fails to resolve. This behavior is suggestive, although far from conclusive, that the growth leads to singularity formation. No sharp transition between singularity formation and either dispersion or stationarity is found, unlike other nonlinear systems that have demonstrated behavior similar to black hole critical behavior at such transitions.

Charged black hole and radiating solutions in entangled relativity

“…( 6) and ( 12) -seems to indicate that the theory is well-behaved with respect to various aspects, such as the Ostrogradsky instability [24,25] or the well-posedness of the initial value problem [26][27][28][29]. Indeed, Einstein-Maxwell-dilaton theories are second-order theories that are notably known to have a well-posed initial-value problem [30,31]. This is similar to what happens with fourthorder f (R) theories [24,27,28].…”

Towards nonlinear axion-dilaton electrodynamics: How can axionic dark matter mimic dilaton-photon interactions?

“…In this case the potential (16) does not vanish, however, the contribution of the axion potential to the equation ( 46) is compensated by the contribution of the electromagnetic field. 3.…”

“…it describes the contribution of the axion field coupled to the aether velocity via the expansion scalar Θ, the argument of the axion potential (16). The third term…”

“…We indicate the states of the axionic system as the equilibrium ones, when φ=nΦ * , since this case corresponds to one of the minima of the potential of the axion field (16). Clearly, now Y = 2πn, thus sin Y = 0 and the right-hand side of the equation ( 46) vanishes.…”

“…The theory of interaction between the electromagnetic and scalar fields has involved into the Lagrangian the terms of the form I 3 = f (ϕ)F mn F mn , where ϕ describes the scalar field, and the function f (ϕ) is the subject of mathematical modeling. The theories linear in the electromagnetic field and nonlinear in the scalar field, have been indicated as Maxwell-dilaton theories (see, e.g., [15][16][17][18][19][20][21][22]). The new true scalar I 4 = φF * mn F mn , where φ is the pseudoscalar field, appeared in the electromagnetic theory in the work [23].…”