My research so far is centred on radiative spacetimes and conformal methods in general relativity. Here are the details.

Geometry of type D radiative spacetimes : I’m interested with the geometry of null congruences in radiative spacetimes and I studied the ingoing radial null geodesics in the Vaidya spacetime. With Jean-Philippe Nicolas, we gave a classification of the integral curves of the ingoing principal directions of the Vaidya metric depending on their limits in the past. In particular we prove that there exists an unique curves that admits a finite limits asymptotically in the past and we proved that this geodesic generates the event horizon of the Vaidya white hole. Then we investigated the behaviour of the horizon in the Vaidya spacetime for a general choice of mass. I proved that it not possible to extend directly these results in a pure radiative type D Robinson-Trautman spacetime.

Asymptotic analysis in Vaidya spacetime for the wave equation : I use the conformal methods developped by Penrose in the 60’s to analyze the aasymptotic behaviour of scalar waves in the Vaidya spacetime. I proved the peeling-off behaviour (that corresponds to the asymptotic regularity) of waves in the Vaidya spacetime, and I constructed the conformal scattering operator for the scalar waves. The scattering operator is proved to be an isomorphism that associates the strace of the rescaled field on the past boundary to its trace on the future boundary.