On Time dependent Black Holes and Cosmological Models from a Kaluza-Klein mechanism

Novel static, time-dependent and spatial-temporal solutions of Einstein field equations, displaying singularities, with and without horizons, and in several dimensions are found based on a dimensional reduction procedure widely used in Kaluza-Klein type theories. The Kerr-Newman black-hole entropy as well as the Reissner-Nordstrom, Kerr and Schwarzschild black-hole entropy are derived from the corresponding Euclideanized actions. A very special cosmological model based on the dynamical interior geometry of a Black Hole is found that has no singularities at t = 0 due to the smoothing of the mass distribution. We conclude with another cosmological model equipped also with a dynamical horizon and which is related to Vaidya’s metric (associated with the Hawking-radiation of black holes) by interchanging t↔ r which might render our universe as a dynamical black hole.