Gravitational stability and extra timelike dimensions - art. no. 065014

Tachyonic Kaluza-Klein modes normally appear from the compactification of e xtra timelike dimensions with scale L, and lead to some instabilities of ph ysical systems. We calculate the contribution of tachyonic gravitons to the self-energies of spherical massive bodies of radius R, and discuss their p ossible gravitational stability. We find that some spherical bodies can be stable at critical radii R = 2 pi Lp for some positive integers p. We also prove the generic property of massive bodies that for the range 0<R<less th an or equal to>piL the gravitational force due to the ordinary massless gra viton exchange is screened by the Kaluza-Klein mode exchange of tachyonic g ravitons.