Gabriel Sánchez Pérez (online): Geometric uniqueness of the Characteristic Problem in General Relativity

In this seminar I will show a geometric uniqueness result of the characteristic Cauchy problem in General Relativity. In the standard Cauchy problem, it is known that two initial data (Σ, h, K) and (Σ′ , h′ , K′ ) such that (Σ, h) and (Σ′ , h′ ) are isometric and the isometry maps K′ into K, give rise to two isometric spacetimes. In order to prove a result of this type in the case of the characteristic problem one needs an abstract notion of the initial data completely detached from the spacetime one wishes to construct. Such abstract formulation is very recent and relies on hypersurface data, and in particular on double null data. In the first part of this seminar the definition of double null data will be presented and I will prove that the definition is complete by showing that any double null data can be embedded in some spacetime. If in addition the constraint equations are fulfilled, the double null data turns out to be embeddable in a spacetime solution of the Einstein equations. Then, the necessary conditions for two double null data to give rise to two isometric spacetimes will be determined. These conditions lead to the definition of isometric double null data. I will finish the seminar by proving that two isometric double null data give rise to isometric spacetimes. This gives a geometric uniqueness notion of the characteristic initial value problem in a fully abstract way.

Contact Oliver Petersen  for the Zoom link.