Gravity, nonlinear gauge fields and charge confinement/deconfinement

We discuss in some detail the properties of gravity (including f (R)-gravity) coupled to non-standard nonlinear gauge field system containing a square root of the usual Maxwell Lagrangian - f₀/2 √-F ². The latter is known to produce in flat spacetime a QCD-like confinement. Inclusion of gravity triggers various physically interesting effects: new mechanism for dynamical generation of cosmological constant; non-standard black hole solutions with constant vacuum electric field and with "hedge-hog"-type spacetime asymptotics, which are shown to obey the first law of black hole thermodynamics; new "tubelike" solutions of Levi-Civita-Bertotti-Robinson type; charge-"hiding" and charge-confining "thin-shell" worm-hole solutions; dynamical effective gauge couplings and confinement-deconfinement transition effect when coupled to quadratic R²-gravity.