Planckian AdS2×S2 space is an exact solution of the semiclassical Einstein equations

The product space configuration AdS2×S2 (with l and r being radiuses of the components) carrying the electric charge Q is demonstrated to be an exact solution of the semiclassical Einstein equations in presence of the Maxwell field. If the logarithmic UV divergences are absent in the four-dimensional theory the solution we find is identical to the classical Bertotti-Robinson space (r=l=Q) with no quantum corrections added. In general, the analysis involves the quadratic curvature coupling λ appearing in the effective action. The solutions we find are of the following types: (i) (for arbitrary λ) charged configuration which is quantum deformation of the Bertotti-Robinson space; (ii) (λ>λcr)Q=0 configuration with l and r being of the Planck order; (iii) (λ<λcr)Q≠0 configuration (l and r are of the Planck order) not connected analytically to the Bertotti-Robinson space. The interpretation of the solutions obtained and an indication on the internal structure of the Schwarzschild black hole are discussed.