Gravitational stability and screening effect from D extra timelike dimensions Original Research Article

We study (3+1)+D dimensional spacetime, where D extra dimensions are timelike. Compactification of the D timelike dimensions leads to tachyonic Kaluza–Klein gravitons. We calculate the gravitational self-energies of massive spherical bodies due to the tachyonic exchange, discuss their stability, and find that the gravitational force is screened in a certain number of the extra dimensions. We also derive the exact relationship between the Newton constants in the full (4+D)-dimensional spacetime with the D extra times and the ordinary Newton constant of our 4-dimensional world.