Seminarium "The Trans-Carpathian Seminar on Geometry & Physics"

Einstein field equations are not conformally invariant. Despite this fact, conformal geometry plays an important role in description of asymptotics of the solutions via so-called Penrose conformal compactification. Moreover, in many cases such conformal compactification of solution is smooth. It turns out that these facts are linked to a fundamental object in conformal geometry, Fefferman-Graham obstruction tensor. I will describe this connection in may talk, together with some interesting implications.