Research in General Relativity

The physical theory of describing gravitational interactions of matter and spacetime is the conglomerate of the ‘here’ and ‘now’ of a physical observer.

My main research field is General Relativity, the physical theory of describing gravitational interactions of matter and spacetime is the conglomerate of the ‘here’ and ‘now’ of a physical observer. Coordinate charts for such observer are generally chosen with three spacial coordinates and one time coordinate. Geometrically, this corresponds to foliating space time in three-dimensional space-like slices meaning one can find one time coordinate be constant on these slices.  In certain conditions (where energies and masses are small) this is like our Newtonian understanding of space and time. In my research, I am working with different coordinate charts where one coordinate is a null (or light-like) coordinate and the other three are spatial coordinates.  In the geometrical picture, the three dimensional surfaces, where the null coordinate is constant, are null (or light-like) hypersurfaces. These null hypersurfaces may be the light cones or cuts of light cones. The advantage of foliating spacetime with null hypersurfaces instead of space-like hypersurfaces is that the former are well adapted to for discussing the causal structure as well as radiation properties of spacetime. Indeed, null foliations were key to understand properties of gravitation radiation and that a physical system (like the merger of two black holes or two neutron stars) can loose mass due to the emmision of gravitational waves.  The  null coordinates leading to our theoretical understanding of this mass loss are the Bondi-Sachs coordinates, which are named after the Herman Bondi and Rainer Sachs who established the mass loss formula. Together with Jeff Winicour, I have written one of the major (online) reviews on the Bondi-Sachs formulation, which can be found in Scholarpedia (a peer reviewed open access encyclopedia)