Maurer-Cartan perturbation theory and scattering amplitudes in general relativity

Andrea Nützi (ETH Zurich)

Jul 07. 2023, 14:00 — 14:50

I will describe a differential graded Lie algebra tailored to study perturbations of Minkowski spacetime, including asymptotics. This differential graded Lie algebra is defined on the conformal compactification of Minkowski spacetime. Its Maurer-Cartan equation is equivalent to the vacuum Einstein equations, and is symmetric hyperbolic including across the boundary of Minkowski spacetime. I will compare this to Friedrich's conformal vacuum field equations, a key difference is that we do not use a conformal factor as an unknown, and null infinity is a fixed locus independent of the unknown. I will then introduce an iteration scheme that gives an order-by-order construction of formal power series solutions about Minkowski. This is based on standard Maurer-Cartan perturbation theory and renormalization of the mass and angular momentum charges. The gauge character is naturally built into the setup. The algebraic framework allows for a rigorous contact with the physics literature on scattering amplitudes. We will see, in low order formal perturbation theory, that these gauge independent amplitudes describe the radiative null asymptotics of the formal solutions.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Spectral Theory and Mathematical Relativity (Thematic Programme)
Piotr T. Chruściel (U of Vienna)
Peter Hintz (ETH Zurich)
Alexander Strohmaier (U Leeds)
Steven Morris Zelditch † (Northwestern U Evanston)