Seminário "Geodesic structure of space-times with integrable singularity and transitions between domains with different signature"

   Singularities in General Relativity (GR) have been an issue for many years. In its conventional sense, singularity implies an ill-defined behavior of, at least, some geometric invariants. Hence, a solution to the problem would be an extended theory that somehow regularizes known GR singularities. However, recently it was realized that there exist GR solutions which are formally singular, but do not show any singular behavior on physical level. One example is a cosmological model with mixture of anti-Chaplygin gas and dust. Another example is a class of space-times with integrable singularity that is a partially regularized counterpart of the Schwarzschild singularity. In this work we study the geodesic structure of a space-time with integrable singularity resulting from collapse of spherically distributed dust into a black-hole-like object. We also argue that some of geodesics continued through the integrable singularity may pass to domains with signature that differs from the ordinary (+  –  –  – ).