Vacuum polarization of massive scalar fields in the spacetime of an electrically charged nonlinear black hole

The approximate renormalized stress-energy tensor of the quantized massive conformally coupled scalar field in the spacetime of an electrically charged nonlinear black hole is constructed. It is achieved by functional differentiation of the lowest order of the DeWitt-Schwinger effective action involving the coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficient a₃. The result is compared with the analogous results derived for the Reissner-Nordstr\"om black hole. It is shown that the most important differences occur in the vicinity of the event horizon of the black hole near the extremality limit. The structure of the nonlinear black hole is briefly studied by means of the Lambert functions.