Off-Diagonal 5D Metrics and Mass Hierarchies with Anisotropies and Running Constants

Abstract

The gravitational equations of the three dimensional (3D) brane world are investigated for both off-diagonal and warped 5D metrics which can be diagonalized with respect to some anholonomic frames when the gravitational and matter fields dynamics are described by mixed sets of holonomic and anholonomic variables. We construct two new classes of exact solutions of Kaluza-Klein gravity which generalize the Randall-Sundrum metrics to configurations with running on the 5th coordinate gravitational constant and anisotropic dependencies of effective 4D constants on time and/or space variables. We conclude that by introducing gauge fields as off-diagonal components of 5D metrics, or by considering anholonomic frames modelling some anisotropies in extra dimension spacetime, we induce anisotropic tensions (gravitational polarizations) and running of constants on the branes. This way we can generate the TeV scale as a hierarchically suppressed anisotropic mass scale and the Newtonian and general relativistic gravity are reproduced with adequate precisions but with corrections which depend anisotropically on some coordinates.