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We evaluate the divergent part of the Vilkovisky-DeWitt effective action forEinstein gravity on even-dimensional Kaluza-Klein spacetimes of the form$M^{4}\times S^{N}$. Explicit results are given for $N$=2, 4, and 6. Traceanomalies for gravitons are also given for these cases. Stable Kaluza-Kleinconfigurations are sought, unsuccessfully, assuming the divergent part of theeffective action dominates the dynamics.Comment: 37 pages, no figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Vilkovisky-DeWitt effective action for Einstein gravity on Kaluza-Klein spacetimes<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>M</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>×</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>

Vilkovisky-DeWitt effective action for Einstein gravity on Kaluza-Klein spacetimesM4×SN