Gravitational stability and screening effect from D extra timelike dimensions

We study (3 + 1) + D dimensional spacetime, where D extra dimensions are ti melike. Compactification of the D timelike dimensions leads to tachyonic Ka luza-Klein gravitons. We calculate the gravitational self-energies of massi ve spherical bodies due to the tachyonic exchange, discuss their stability, and find that the gravitational force is screened in a certain number of t he extra dimensions. We also derive the exact relationship between the Newt on constants in the full (4 + D)-dimensional spacetime with the D extra tim es and the ordinary Newton constant of our 4-dimensional world. (C) 2001 El sevier Science B.V. All rights reserved.