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The gravitational effect of vacuum polarization in space exterior to aparticle in (2+1)-dimensional Einstein theory is investigated. In the weakfield limit this gravitational field corresponds to an inverse square law ofgravitational attraction, even though the gravitational mass of the quantumvacuum is negative. The paradox is resolved by considering a particle of finiteextension and taking into account the vacuum polarization in its interior.Comment: 10 pages, LaTeX, Report: UPR-0540-T, To appear in Physica Script

Inverse square law of gravitation in (2 + 1)-dimensional space–time as a consequence of Casimir energy