Seminarium Kosmologia i Fizyka Cząstek

It is explicitly shown under which conditions flat and Ricci-flat spacetimes as well as maximally symmetric manifolds are exact solutions of the equation of motion (EOM). We find that well-known physical spacetimes like Schwarzschild, Kerr, (Anti-) de Sitter serve as solutions for standard matter content, when the EOM does not contain Riemann tensor alone. In dimension higher than four we can also have Anti-de Sitter solutions in the presence of positive cosmological constant. I will pedagogically show how to obtain these exact solutions. Furthermore, for another version of theories from this class, with terms written in the Weyl basis, Friedmann-Robertson-Walker (FRW) spacetimes are also exact solutions (exactly in the same way like in Einstein theory), when the matter content is given by conformal matter (radiation). I will also comment on rather inevitable presence and universality of singularities and possible resolution of them in finite and conformally invariant theories. ``Delocalization" is proposed as a way to solve the black hole singularity problem. In order to solve the problem of cosmological singularities it seems crucial to have a conformally invariant or asymptotically free quantum gravitational theory.