Vacuum polarization of the electromagnetic field near a rotating black hole

The electromagnetic field contribution to the vacuum polarization near a rotating black hole is considered. It is shown that the problem of calculating the renormalized average value of the stress-energy tensor 〈$T_{\mu }$ ${\mathrm{}}^{\nu }$ ${〉}^{\mathrm{ren}}$ for the Hartle-Hawking vacuum state at the pole of the event horizon can be reduced to the problem of electro- and magnetostatics in the Kerr spacetime. An explicit expression for 〈$T_{\mu }$ ${\mathrm{}}^{\nu }$ ${〉}^{\mathrm{ren}}$ at the pole of the event horizon is obtained and its properties are discussed. It is shown that in the case of a nonrotating black hole the Page-Brown approximation for the electromagnetic stress-energy tensor gives a result which coincides at the event horizon with the exact value of 〈$T_{\mu }$ ${\mathrm{}}^{\nu }$ ${〉}^{\mathrm{ren}}$. .AE