Seminar

# From null geodesic to gravitational scattering [An alternative route from BMS to soft theorems via ambitwistors and strings]

#### General Relativity, Geometry and Analysis: beyond the first 100 years after Einstein

#### 17 September 10:00 - 11:00

#### Lionel Mason - Oxford University

This talk has two parts giving examples of the same theme, that the scattering of null geodesics can be used to determine the scattering of the gravitational field. The first is a 2+1 dimensional model concerning asymptotically de Sitter solutions to the Einstein-Weyl equations. We prove that the scattering of null geodesics from past to future infinity determines a diffeomorphism from the Riemann sphere to itself modulo Mobius transfomations. We prove that this correspondence is invertible: if such a map is not too large, then we can reconstruct an Einstein-Weyl space-time whose scattering map is the given one. [This is joint work with Claude LeBrun. ] The second part concerns how the correspondence can be extended to higher dimensions. This uses spaces of complex null geodesics, ambitwistors, and string based formulae to calculate scattering perturbatively on asymptotically simple space-times. We show that, in the case of soft gravitons (low energy), again the scattering can be encoded in a diffeomorphism from past to future null infinity that is a supertranslation. This can be used to obtain a correspondence between the BMS group and soft theorems, but the interpretation is rather different from that of Strominger's, in that it does not arise from symmetry considerations. [This is joint work with Geyer & Liptsein.]

Organizers

Lars Andersson

Max Planck Institute for Gravitational Physics (Albert Einstein Institute)

Mattias Dahl

KTH Royal Institute of Technology

Philippe G. LeFloch

Sorbonne University

Richard Schoen

University of California, Irvine