Princeton Gravity Initiative - Symmetry Algebras and Black Holes in Self Dual Gravity - Noah Miller - Harvard University

Dec 11, 2023, 12:30 pm1:30 pm
PGI Space - 4th Floor Jadwin Hall
Faculty, post docs, grads


Event Description

This talk will explore recent insights into the structure of classical self dual gravity and non-Kerr-Newman black holes from the study of celestial holography and scattering amplitudes. “Self dual gravity” refers to a theory in which the Riemann curvature 2-form is required to be invariant under the Hodge star operator. Such spacetimes are necessarily 4-dimensional and satisfy the vacuum Einstein equation.


Self dual gravity is an integrable theory and enjoys an infinite tower of infinite dimensional symmetry algebras, known collectively as the Lw_{1+infinity} algebra. We will explain how this algebra acts on the classical spacetime metric using a set of quasinormal modes known as “integer modes.” We will explain how these transformations can be understood as “half” gauge transformations which moves the system around the space of self dual metrics.


We will also discuss self dual black hole metrics in (2,2) signature, known as (Kerr) Taub NUT spacetimes. Analytic continuation to (2,2) signature has long been a useful tool in the computation of scattering amplitudes, enabling the use of on-shell methods to calculate amplitudes far more efficiently than Feynman diagrammatics. Here we’ll discuss the global structure of the (2,2) Taub NUT metric (a strange thing to consider, to be sure) and show how its linearization can be computed by a single on shell radiative diagram. 


Time permitting we will also discuss the eternally accelerating “C metric” black hole spacetime with a boost Killing symmetry.