Asymptotically de Sitter and anti-de Sitter Black Holes with Confining Electric Potential

We study gravity interacting with a special kind of QCD-inspired nonlinear gauge field system which earlier was shown to yield confinement-type effective potential (the "Cornell potential") between charged fermions ("quarks") in flat space-time. We find new static spherically symmetric solutions generalizing the usual Reissner-Nordstroem-de-Sitter and Reissner-Nordstroem-anti-de-Sitter black holes with the following additional properties: (i) appearance of a constant radial electric field (in addition to the Coulomb one); (ii) novel mechanism of {\em dynamical generation} of cosmological constant through the non-Maxwell gauge field dynamics; (iii) appearance of confining-type effective potential in charged test particle dynamics in the above black hole backgrounds.