Model for nonspherical collapse and formation of black holes by emission of neutrinos, strings, and gravitational waves

We present a general relativistic exact model for the spacetime external to an axisymmetric bounded distribution of collapsing matter whose rate of mass decrease is a constant that, when vanishing, yields a Schwarzschild solution. Einstein's field equations actually require the existence of a timelike shell in the equatorial plane, whose stress-energy tensor is constituted by two independently conserved terms, corresponding to the emission of neutrinos and strings on the shell. An extension of this model can be achieved to include the emission of gravitational waves that provides a mechanism by which the rate of mass decrease goes to zero with the formation of a Schwarzschild black hole.