F(R)-gravity: “einstein frame” lagrangian formulation, Non-standard black holes and QCD-like confinement/deconfinement

Abstract

We consider f(R)=R+R2 gravity interacting with a dilaton and a special non-standard form of nonlinear electrodynamics containing a squareroot of ordinary Maxwell Lagrangian. In flat spacetime the latter arises due to a spontaneous breakdown of scale symmetry and produces an effective chargeconfining potential. In the R+R2gravity case, upon deriving the explicit form of the equivalent local “Einstein frame” Lagrangian action, we find several physically relevant features due to the combined effect of the gauge field and gravity nonlinearities such as: appearance of dynamical effective gauge couplings and confinementdeconfinement transition effect as functions of the dilaton vacuum expectation value; new mechanism for dynamical generation of cosmological constant; deriving nonstandard black hole solutions carrying additional constant vacuum radial electric field and with non-asymptotically flat “hedge-hog”-type spacetime asymptotics.