Abstract: General Relativity admits a well-posed characteristic initial value problem, where data is given on two transverse, null hypersurfaces. In this seminar, a new approach in which the initial data is defined abstractly and in a fully diffeomorphism and gauge-covariant way is presented.
In order to achieve this we employ the so-called hypersurface data formalism, a framework in which one can study general hypersurfaces of any causal character from an abstract point of view (i.e. independent of any spacetime notion).
Our abstract geometrization puts the characteristic problem on a similar footing as the standard Cauchy problem in General Relativity, in the sense that the initial data has been completely detached from the spacetime one wishes to construct.