Masters Thesis Defense by Rögnvaldur Konráð Helgason

Title: On Carrollian Expansion of Gravity

Abstract: Carrollian geometry is a type of non-Lorentzian geometry that has gained considerable traction in recent years. It has important applications to flat space holography due to its relation to null hypersurfaces as well as to the physics of black holes and cosmology.

One arrives at Carrollian geometry by taking a small speed of light expansion of Riemannian geometry and one arrives at Carrollian gravity in the same manner via the small speed of light limit of general relativity.

The goal of this thesis is threefold: to complete the full derivation of NLO equations of motion of the Carroll expansion of GR (previously done to truncated order), to show that the Carrollian expansion of Schwarzschild black holes can be derived from general vacuum solutions to the evolution equation of the theory, and to expand the Kerr metric for both the electric and magnetic limit of the Carrollian expansion.

In order to expand the Kerr metric, one needs to include odd powers of c in the Carrollian expansion which will be explored in this thesis as well.

Supervisors: Prof. Niels Obers and Dr. Emil Have 

Censor: Prof. Marta Orselli