Abstract
Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in D-dimensional gravity with a chain of n Ricci-flat internal spaces are considered. Their special cases and properties are discussed, in particular, the predicted Coulomb law violation. A family of multidimensional dilatonic black-hole solutions is singled out, depending on two integration constants (related to black hole mass and charge) and three free parameters of the theory (the physical and internal space dimensions and the dilaton coupling constant). The black-hole solutions are shown to be stable under small perturbations preserving spherical symmetry, while other solutions, possessing naked singularities, turn out to be catastrophically unstable.
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