Christodoulou The vacuum Einstein equations for gravitation shall be studied without imposing any symmetry or restriction on the size of the initial data. The structure of spacetime singularities resulting from a trapped region shall be explored. Initial conditions which leads in evolution to the formation of trapped regions shall be sought. The possibility of singularity formation not resulting from a trapped region shall be investigated. Criteria for the local extendibility of solutions shall be sought to which improve known results. Also, an effort shall be made to establish a variational characterization of the Kerr solution. The work on the spherically symmetric Einstein equations with matter represented by the two-phase fluid model shall be continued with the aim of characterizing the initial conditions leading to the two alternatives: black hole or neutron star formation. Finally, the two-phase model without the restriction to spherical symmetry shall be studied in the framework of special relativity.
These mathematical studies will provide insight into difficult fundamental questions in gravitation theory. ***