Dilatonic brane-world black holes, gravity localization, and Newton's constant

The family of brane-world solutions of (d + 1)-dimensional dilatonic gravity is presented. It includes a hat brane with a small cosmological constant and (anti-)de Sitter brane, dilatonic brane-world black holes [Schwarzschild-(anti-)de Sitter, Kerr, etc]. Gravitational and dilatonic perturbations around such branes are found. It is shown that near the dilatonic brane-world black hole gravity may be localized in a standard form. The brane corrections to Newton's law are estimated. The proposal to take into account the dilaton coupled brane matter quantum effects is made. The corresponding effective action changes the structure of a 4D de Sitter wall. Renormalization-group flow of the four-dimensional (4D) Newton constant in IR and UV is briefly discussed.