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Gravitational Effective Field Theories and Microscopic Description of Superradiance

Periodic Report Summary - GRAVEFTMICS (Gravitational effective field theories and microscopic description of superradiance)

The tantalising similarities between the physics of black holes and the properties of soap bubbles and fluid lumps have been observed from old and motivated approaches like the membrane paradigm with useful applications in astrophysical systems. However only recently a formal and precise duality between gravity and hydrodynamics was finally established and goes nowadays by the name of gauge / fluid correspondence.

Navier-Stokes equations encode in a certain regime Einstein's equations! The lesson to take home is that gravity has a holographic hydrodynamic description in terms of a near-equilibrium and long-wavelength effective description of a quantum field theory. This provides a powerful tool to study black holes in a hydrodynamic setup.

In the last year we have explored this correspondence in two papers published in JHEP. We studied the stability of rotating plasma balls that are holographic duals to certain black holes that live in an asymptotically anti-de Sitter background. We found that rotating plasma balls are unstable against m-lobed perturbations for rotations above a critical value. This unstable mode signals a bifurcation to a new branch of non-axisymmetric stationary solutions which resemble a 'peanut-like' rotating plasma. The gravitational dual of the rotating plasma ball must then be unstable and possibly decay to a non-axisymmetric long-lived black hole. This instability provides therefore a mechanism that bounds the rotation of the black holes.

A truly fascinating property of black holes is their ability to enter in the quantum realm domain. Indeed, in the 1970's Stephen Hawking famously proved that when quantum effects are considered, black holes have temperature, entropy and do evaporate. Moreover, the spectrum of the evaporation products is thermal, hinting at a statistical averaging over microscopic states behind the scenes.

In this context an interesting proposal - known as the Kerr / CFT correspondence - was put forward. Using holographic gravity / gauge theory techniques applied on the near horizon geometry of the Kerr solution, this correspondence claims to finally understand the statistical origin of the entropy of extreme Kerr black holes. This proposal considers very strong and unique assumptions on the boundary conditions of the gravitational field that were not totally justified. Boundary conditions are required to predict the time evolution of initial data in the system.

Together with the scientist in charge and a PhD student, we determined these boundary conditions by studying the asymptotic behaviour of the solutions of perturbed Einstein's equations. We found that the boundary conditions proposed ad hoc in the original paper did not lead to a well-posed initial value problem. This is a fundamental result since it demonstrates that the Kerr / CFT proposal is still not the final answer for the important question of the statistical description of the Bekenstein-Hawking black hole entropy.

It has been conjectured that higher-dimensional rotating black holes become unstable at a sufficiently large value of the rotation, and that new black holes with pinched horizons appear at the threshold of the instability that was coined as the ultraspinning instability. In two papers (one with the scientist in charge) we have found the explicit proof of this instability and studied its properties in detail. This was a very important open problem in the area since the last decade. As an important outcome of our research we also found that Hawking's rigidity theorem is saturated in higher dimensions, and found evidence for the existence of new families of black hole solutions. We will keep exploring this topic.

Two of these papers were done in collaboration with the scientist in charge. Three of them were done in collaboration with two PhD students, and four of the papers involved authors from other institutions. These works were presented in a total of 8 seminars / workshops.