## Periodic Reporting for period 4 - NewNGR (New frontiers in numerical general relativity)

Période du rapport: 2020-03-01 au 2021-02-28

It turns out that GR beyond the astrophysical setting is poorly understood. For instance, black holes can have new shapes and they may suffer from dynamical instabilities whose endpoints are not known. Moreover, gravity in AdS space exhibits new phenomena, which are not present in the astrophysical context, and which often arise in the full non-linear regime of the theory. Hence numerical methods are the only tool available to study them. The main aim of this project is to get a better understanding of gravity, as described by GR, in scenarios that naturally arise in the context of the AdS/CFT correspondence, namely higher dimensional and/or AdS spaces, using numerical methods. This project has two general objectives:

1) Develop new numerical codes to study time-dependent spaces.

2) Find new types of equilibrium black holes.

We have successfully accomplished our goals in Objective 1). First, we have managed to evolve the various instabilities that afflict certain asymptotically flat black holes in 5, 6 and 7 dimensions and found compelling evidence for their endpoints. We have also considered collisions of stable spinning black holes in 6 and 7 dimensions. In all these cases, we showed that if the initial angular momentum is large enough, a naked singularity forms via the Gregory-Laflamme instability. This result implies that Penrose’s weak cosmic censorship conjecture is violated in higher dimensions and, consequently, general relativity generically loses its predictive power. However, this loss of predictivity is minimal, only involving microscopic amounts of mass. We have also developed a general method to solve the Einstein equations in AdS as an initial boundary value problem. This method allows us to carry out large scale simulations and use AMR. With this new code, we have investigated the non-linear evolution of generic perturbations of global AdS beyond spherical symmetry. We also studied the process of black hole formation in confining backgrounds and the equilibration of large perturbations of black branes. Our results allowed us to get a better understanding of the applicability of hydrodynamics in strongly coupled gauge theories. In terms of Objective 2), we have developed a general code to construct new types of black holes in 10 and 11 dimensions and study their properties near the region where they merge with new types of black holes with new shapes. This work has allowed us to extract new predictions for the AdS/CFT correspondence and understand how the field theory “detects” the changes of shape in black holes. In addition, we have developed a new method to find black holes in theories of gravity with multiple speeds of propagation and applied it to construct rotating black holes in Einstein-Aether theory of gravity.

Our work has been published in high impact journals and our GRChombo code is publicly available on our website: http://www.grchombo.org/.