WMBH · Waves, mean flows and black holes
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2020-04-01 → 2022-06-06
- EU contribution
- €196,708
- Participants
- 1
- Scheme
- MSCA-IF
Lines connect the coordinator with its partners.
Results in brief
Waves, mean flows and black holes
The problem of waves propagating in an inhomogeneous background is ubiquitous in physics: from gravitational waves around black holes, to ocean surface waves in mean flows or acoustic waves in media with a complex microstructure. Such a background often induces resonances: a discrete set of frequencies that strongly respond to a given excitation. A large class of applications of resonances consists in identifying them to obtain information about the background. For instance, the spectrum of gravitational waves can be used to obtain the mass and angular momentum of a black hole, or one can send acoustic waves to image defects inside a given material. In mathematics, this kind of imaging technique is called an inverse problem: from the knowledge of the wave resonance frequencies, one would like to reconstruct the structure of the background. In this context, a key question is that of the stability of these resonance frequencies: how strongly are they changed when the background varies? The objective of this project is to develop general tools to address this problem in the seemingly unrelated contexts it arises. For this, we used a combination of differential geometric and spectral theoretic methods. This project tackled this question in two distinct contexts: gravitational waves around black holes, and acoustic waves in periodic structures. In the former case, geometry is used to describe the black hole space-time (i.e. its gravitational field). In the latter, the geometry is that of the reciprocal space, that is, after a Fourier transform the background is characterize by a curvature called the Berry curvature.
Data: CORDIS, © European Union
Project objective
Black holes are among the most fascinating objects of the Universe. They are today at the core of our understanding of gravitation. They provide essential hints towards a theory of quantum gravity. They constitute the main emission source of gravitational waves, which will play a central role in future astrophysics. Black holes are also central in mathematical relativity, and the proof of their stability is still today a challenging problem. In the last decades, several analogies between gravity and fluid mechanics have been developed. This interdisciplinary approach has led to many innovative methods and successful results, which have deepened our understanding of black holes, fluids or superfluids. More recently, such an analogy was used by various experimental groups, which were able to successfully reproduce several key effects of black hole physics using fluid systems. The aim of this project is to develop the mathematical tools to open a new avenue in this interdisciplinary field: the understanding of nonlinear dynamics. In other words, how waves are affected by a background flow or spacetime, and subsequently modify their dynamics. It will focus on three research directions: the analogue of the Hawking effect, superradiant instabilities, and resonances. This project will bring an experienced researcher in analogue models in a strong mathematical physics group, within the Institute of Mathematics of Burgundy (IMB). The objective is to exploit modern mathematics to develop new tools for the joint analysis of black holes and fluids. It will rely on the one hand on mathematical methods of integrable models, and spectral theory of non self-adjoint operators, two fields in which the host group has a traditionally strong expertise, and on the other hand on the knowledge in General Relativity and analogue models of the experienced researcher.
Original text from CORDIS.
Participants
- COMMUNAUTE D' UNIVERSITES ET ETABLISSEMENTS UNIVERSITE BOURGOGNE - FRANCHE - COMTE · BesanconCoordinatorFrance
Links
Data: CORDIS, © European Union