MG11 
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A new exact static thin disk with a central black hole

A new exact solution of the Einstein equations corresponding to the superposition of an annular static thin disk with a central black-hole is presented. All the metric functions of the superposition are explicitly computed and the obtained expressions are simply written in terms of oblate spheroidal coordinates. The obtained solution represents an infinite annular thin disk around the Schwarszchild black-hole. The mass of the disk is finite and the energy-momentum tensor agrees with all the energy conditions.

A new family of solutions for cylindrical gravitational waves

A new family of solutions of the Einstein vacuum equations for cylindrical gravitational waves is presented. The solutions are obtained by considering a generalized Einstein-Rozen line element in such a way that one of the metric functions is solution of the classical one-dimensional wave equation. By taking two independent solutions of this equation, we make a transformation that leads the Einstein equations to the usual Einstein-Rozen form. We then introduce a new coordinate transformation that permits to integrate exactly all the Einstein equations. The obtained solutions can be simply expressed in terms of Legendre functions of first and second class.