We study the third quantization of a Brans-Dicke toy model, we calculate the number density of the universes created from nothing and found that it has a Planckian form. Also, we calculated the uncertainty relation for this model by means of functional Schrödinger equation and we found that fluctuations of the third-quantized universe field tends to a finite limit in the course of cosmic expansion.

We present two new classes of axisymmetric stationary solutions of the Einstein-Maxwell-Dilaton equations with coupling constant α 2 = 3. Both classes are written in terms of two harmonic maps λ and τ . λ determines the gravitational potential and τ the electromagnetic one in such a form that we can have an arbitrary electromagnetic field. As examples we generate two solutions with mass (M ), rotation (s) and scalar (δ) parameters, one with electric charge (q) another one with magnetic dipole (Q) parameter. The first solution contains the Kerr metric for q = δ = 0.

We consider noncommutative quantum cosmology in the case of the low-energy string effective theory. Exacts solutions are found and compared with the commutative case.The Noncommutative quantum cosmology is considered in the case of the low-energy string effective theory. Exacts solutions are found and compared with the commutative case.