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We briefly outline several main results concerning various new physicallyrelevant features found in gravity -- both ordinary Einstein or $f(R)=R+R^2$gravity in the first-order formalism, coupled to a special kind of nonlinearelectrodynamics containing a square-root of the standard Maxwell Lagrangian andknown to produce charge confinement in flat spacetime.

Dynamical Couplings and Charge Confinement/Deconfinement from Gravity Coupled to Nonlinear Gauge Fields