Vacuum polarization of massive spinor and vector fields in the spacetime   of a nonlinear black hole
  Building on general formulas obtained from the approximate renormalized effective action, the stress-energy tensor of the quantized massive spinor and vector fields in the spacetime of the regular black hole is constructed. Such a black hole is the solution to the coupled system of nonlinear electrodynamics and general relativity. A detailed analytical and numerical analysis of the stress-energy tensor in the exterior region is presented. It is shown that for small values of the charge as well as large distances from the black hole the leading behavior of the stress-energy tensor is similar to that in the Reissner-Nordstr\"om geometry. Important differences appear when the inner horizon becomes close to the event horizon. A special emphasis is put on the extremal configuration and it is shown that the stress-energy tensor is regular inside the event horizon of the extremal black hole. 
Jerzy Matyjasek