PhD defense by Shanzhong Han

The Weyl double copy and black holes

Using spinor formalism, we investigate the profound connection between gravity theory and gauge theory in this thesis. We concentrate on the Weyl double copy prescription. Given that higher spin massless free-field spinors can be constructed from spin-1/2 spinors (Dirac-Weyl spinors) and scalars, we introduce a map between Weyl fields and Dirac-Weyl fields and determine the corresponding Dirac-Weyl spinors in a given empty spacetime. Specifically for non-twisting vacuum Petrov type N and type D solutions, our findings elucidate a number of fundamental properties that were previously unknown. We systematically reconstruct the Weyl double copy for these solutions and demonstrate the significance of the zeroth copy in connecting gravity fields with a single copy and degenerate Maxwell fields with the Dirac-Weyl fields in curved spacetime.

Moreover, we investigate the Weyl double copy relation for vacuum solutions of the Einstein equations with a cosmological constant using our new approach in which Dirac-Weyl fields are considered fundamental units. Our research demonstrates that the single and zeroth copies satisfy conformally invariant field equations in conformally flat spacetime and that the zeroth copy retains its importance in connecting gravity fields with a single copy and Dirac-Weyl fields with degenerate electromagnetic fields in curved spacetime. In addition, we find that the zeroth copy plays an important role in time-dependent radiation solutions, especially for Robinson-Trautman gravitational waves. In the limit of weak fields, the zeroth copy carries additional information indicating whether the sources of gravitational waves are time-like, null, or space-like. Finally, we present an overview of our ongoing work and future research directions.

PhD committee:
Chair: Matthias Wilhelm
Members: Cynthia Keeler and Henrik Johansson

Supervisor: Niels Obers