Fri, 28 Feb 2025
14:30
N3.12

Flux-balance Laws in Flat Space Holography

Adrien Fiorucci
(Ecole Polytechnique)
Further Information

Part of a Carrollian day in wonderland 9.15am-5pm.

Abstract

The main challenges in constructing a holographic correspondence for asymptotically flat spacetimes lie in the null nature of the conformal boundary and the non-conservation of gravitational charges in the presence of bulk radiation. In this talk, I shall demonstrate that there exists a systematic and mathematically robust approach to understanding and deriving the associated flux-balance laws from intrinsic boundary geometric considerations — an aspect of crucial importance for flat-space holography, as I shall argue during the presentation. 

For self-containment, I shall begin by reviewing key aspects of the geometry at null infinity, which has been termed conformal Carroll geometry. Reviving Ashtekar’s old statement, I shall emphasise that boundary affine connections possess degrees of freedom that precisely serve as the sources encoding radiation from a holographic perspective. I shall conclude by deriving flux-balance laws in an effective field theory framework at the boundary, employing novel techniques that introduce “hypermomenta” as responses to fluctuations in the boundary connection. The strength of our formalism lies in its ability to perform all computations in a manifestly coordinate- and Weyl-invariant manner within the framework of Sir Penrose’s conformal compactification.

Fri, 28 Feb 2025
12:00
L5

Extreme horizons and Hitchin equations

Maciej Dunajski
(Cambridge)
Abstract
We establish the rigidity theorem for black hole extremal horizons, and prove that their compact cross-sections must admit a Killing vector field. The intrinsic Riemannian geometry of extremal horizons admits a quasi-Einstein structure. We shall discuss another class of such structures  corresponding to projective metrizability, where global results can be obtained. In this case the quasi-Einstein structure is governed by the Hitchin equations.
 

 

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