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. 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" wormhole solutions; dynamical effective gauge couplings and confinement-deconfinement transition effect when coupled to quadratic R^2-gravity.