MSc Defense: Gowtham Rishi Mukkamala

Title: Uses of Killing Vectors and Tensors in General Relativity 

Abstract: Symmetries in General Relativity and their connection to conserved quantities and particle dynamics are studied through Killing vectors, conformal Killing vectors and Killing tensors. These objects are first studied on simple metrics such as the 2-sphere and flat space. Using a stereo graphic projection the complex structure of the 2-sphere is unveiled and is used to calculate the Killing vectors, conformal Killing vectors and Killing tensors. Then these objects are applied to study the symmetries on the Schwarzschild metric, which are characterised by four Killing vectors. 

Furthermore, we also study how these Killing vectors allow the geodesic equation to be cast into a first-order form. Which is then perturbed in Newton’s constant G to calculate the scattering angles for a test particle in the Schwarzschild geometry up to order G^3. Finally, the symmetries in the Kerr metric are examined where, in addition to two Killing vectors, an extra “hidden” symmetry is found from a Killing tensor. This “hidden” symmetry produces the Carter constant, which is used to cast the geodesic equation into a first-order form. The geodesic equation is then perturbed in G and the spin of the black hole: a  to compute scattering angles below order G^2 a^2.

Supervisors: Cristian Vergu and Emil Bjerrum-Bohr 

Censor: Marta Orselli