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From fluid dynamics to quantum gravity

Periodic Reporting for period 1 - FDtoQG (From fluid dynamics to quantum gravity)

Reporting period: 2015-08-03 to 2017-08-02

Since the seminal work of Unruh, it is known that waves propagating in a moving fluid behaves as waves in a gravitational field, and in particular, that of a black hole. This allows us to mimic several black hole phenomena in laboratory setups. The domain exploiting this idea, called ?analogue gravity? has recently undergone a rapid expansion, due to several experimental results in different media, such as water waves, optical fibers or Bose-Einstein condensates. However, these experiments raise many new theoretical questions to be properly understood, as well as to conduct new ones.

Understanding and performing such experiments are of great value for fundamental physics. These analogue in fluids allows us to study and observe phenomena that are currently out of reach in astrophysics. Observing them in a fluid confirm there robustness, giving us more confidence it must exist in the universe. But they also give us new insights and hints on the possible difficulties, or new effects that are currently not suspected.

The aim of this project was to understand the theoretical aspects of the analogues of black hole effects and cosmology in fluids. We have focused on three main effects: Hawking radiation, black hole superradiance, and particle production in cosmology. The project has not only advanced the theoretical understanding of these effects, but it has also provided an experimental verification of superradiance using water waves.
Since the beginning of the project, I conducted 7 studies, with various collaborators, each leading to a publication.

1) I developed new tools to study particle production in cosmology when the universe undergoes a bounce, that is, a transition from a contracting to an expanding phase. In these types of problem, the dynamics of space-time is implemented using semiclassical solutions. Unfortunately, these are singular on a bounce (it is a turning point). To avoid this problem, we constructed semiclassical solutions in momentum representation, which are now regular. Essentially, this amounts to using (extrinsic) curvature instead of volume as a degree of freedom of the universe. We show what is the domain of validity of these solutions, under what conditions it becomes equivalent to the usual ones, and how to exploit them to describe particle production near a bounce. This has lead to the single authored publication A. Coutant, Phys. Rev. D 93 (2016) 043520.

2) We studied the general mechanism of appearance of unstable mode in the presence of superradiance. We detailed this mechanism in both explicit and abstract general examples. We also established a clear link between these modes and, quasi-normal modes, which are essential in black hole physics. The link was established by a careful study of the analytic properties of the resolvent. We therefore clarified the relation between the mathematical spectral theory and stability analysis of black holes. This has lead to the publication A. Coutant, F. Michel, and R. Parentani, Class. Quant. Grav. 33 (2016) 125032.

3) We studied the modification of the Hawking effect in fluids whose velocity do not surpasses the speed of sound, i.e. without a horizon. Naively, the effect should be entirely absent. However, due to dispersive effects, it is not, and the Hawking effect leaves an imprint. Characterising this imprint was an open question so far. To proceed, we developed a new mathematical tool to study the scattering in such flows (a generalization of the Bremmer series). This lead to the publication A. Coutant and S. Weinfurtner, Phys. Rev. D 94 (2016) 064026.

4) We studied (theoretically) a new possible experimental setup for detecting superradiance in fluids. The model is based on the study of wave scattering on a rotating cylinder immersed in the fluid. In close analogy to the Zeldovich' cylinder, low frequency waves shows superradiance. We analyzed in detail this model, its stability, and how the value of the cylinder's impedance affects superradiance. The results are presented in the publication V. Cardoso, A. Coutant, M. Richartz, S. Weinfurtner, Phys. Rev. Lett. 117 (2016) 271101.

5) We performed an experimental verification of black hole superradiance in a water wave analogue of a rotating black hole. For this we image and analyze both the flow of a draining bathtub vortex, and waves propagating on it. We show that in some cases, the energy carried by the waves is amplified, showing that these waves have extracted energy from the vortex. We show that this process satisfies the superradiant condition of black holes. We study how the amplification or absorption varies with the frequency and angular momentum of the wave. These results have been published in T. Torres, S. Patrick, A. Coutant, M. Richartz, E. W. Tedford, and S. Weinfurtner, Nature Phys., 13 no. 9, 833836 (2017).

6 and 7) We analyzed the analogue of the Hawking effect in the regime of low frequencies where it is the most visible. In this regime, side effects are also significant, and the properties of the Hawking radiation are significantly altered by dispersion, greybody factors, or non-zero temperatures. We obtained exact mathematical results, that allows us to describe these side effects, and how they affect the observables. We conducted the analysis in two important models: the Korteweg-de Vries model describing water waves, and the Bogoliubov-de Gennes model describing sound in Bose-Einstein condensate
This project has significantly contributed to the field both at the experimental and theoretical level. The main result was the experimental observation of black hole superradiance in a water wave analogue of a rotating black hole. We have also published several theoretical studies, that provided a detailed understanding of current experimental results (in water and in Bose-Einstein condensates). This allows us to compare fluid experiments with the same effect expected in black hole physics, and therefore extending our understanding of them. The conducted work will have an important impact on the analogue gravity community, and will allow the conduction of new experiments to further challenge the robustness of exotic phenomena of black hole physics.
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