Abstract
We investigate the behavior of small perturbations around the Kaluza–Klein monopole in the five-dimensional space–time. We find that the even parity gravitational wave does not propagate in the five-dimensional space–time with Kaluza–Klein monopole provided that the gravitational wave is constant in the fifth direction. We conclude that a gravitational wave and a U(1) magnetic monopole do not coexist in five-dimensional Kaluza–Klein space–time.
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