We consider one-loop effects in general relativity which result in quantum long-range corrections to the Newton law, as well as to the gravitational spin-dependent and velocity-dependent interactions. Some contributions to these effects can be interpreted as quantum corrections to the Schwarzschild and Kerr metric.Comment: a reference added; 14 pages, 7 figure

We have found the graviton contribution to the one-loop quantum correction to the Newton law. This correction results in interaction decreasing with distance as 1/r^3 and is dominated numerically by the graviton contribution. The previous calculations of this contribution to the discussed effect are demonstrated to be incorrect.Comment: 10 pages, 5 figures; numerical error corrected, few references adde

We calculate the transverse muon polarization in the decay K ± → π 0 µ ± ν induced by the electromagnetic two-photon final-state interaction. For the central part of the Dalitz plot the typical value of this polarization is about 4 × 10 −6 .

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