Dias STFC Fellowship research grant

Black hole (BH) thermodynamics and Hawking quantum radiation suggest the existence of a statistical or microscopic description of BHs behind the scenes. This description necessarily requires quantum gravity. BHs have an entropy (a quantity that measures the disorder of the system) proportional not to its volume (as usual in other systems) but instead to its horizon's area. This suggests that the quantum information of the BH is distributed over a surface rather than on a volume. This motivates the holographic principle according to which quantum gravity in a given volume should have a dual equivalent description in terms of a quantum field theory (QFT) on its boundary surface. The gravity/gauge theory or holographic dualities (correspondences or maps) are a concrete realization of this holographic principle. Take (quantum) gravity on an anti-de Sitter (AdS) universe. An AdS background has a gravitational barrier that reflects back any object: effectively, gravity is confined inside a box. The idea behind the holographic principle is that the information inside the AdS box, where we have typically a BH, is projected (as a hologram) into the boundary wall. There, the same information is encoded in a QFT (ie, gauge theory). So we can write the same information in two different scientific languages (the gravitational and the QFT). It is fundamental to develop the dictionary between these two languages to understand phenomena in one theory that involves hard computations by reformulating it on the dual language where computations can be easier. This proposal will develop this dictionary to understand properties of BHs and QFTs (of the kind that describe the strong nuclear interactions being studied at the Large Hadron Collider - LHC - at CERN). As can be inferred from the description above, BHs play an essential role in these holographic correspondences. On the gravity side of the duality, BHs are the most extreme gravitational objects. On the other hand, because they have Hawking temperature, on the QFT side they are the heating source that excites the system up to the point where energetic phenomena appears. In particular, BHs do exhibit other phenomena related to the emission of radiation (and that is actually typically entangled with Hawking radiation). This is known as superradiance. This is a process whereby a electromagnetic or gravitational wave scatters a BH and gets amplified because it extracts energy and spin from the BH. In addition, if the BH is confined inside the AdS box, the previously amplified radiation will be reflected back to the BH where it gets further amplified. These multiple amplifications/reflections lead to an instability. Remarkably, we still do not know much about how such a BH with radiation orbiting around it will evolve in time and what is the endpoint of this unstable system. This proposal proposes to fill this gap in our knowledge and aims to find the answer to these open questions. LHC at CERN is colliding two beams of heavy ion collisions and observing the byproducts of this violent crash. Within the holographic correspondence, this process maps to the collision of two gravitational shock waves (ie two disks or beams of gravitational energy) that is described by Einstein's equations. This proposal will thus use Einstein's equations to simulate these collisions using the aforementioned dual scientific language. In particular, these gravitational numerical simulations will allow to follow the time evolution of the system after the collision and study how the system evolves towards its final state where it equilibrates and cools down. This might be particularly useful to help interpret what is happening at LHC because the standard technical tools that the QFT scientists at LHC have (and that are extremely successful in other contexts where the quantum system is at equilibrium) are not applicable in such violent out-of-equilibrium stages that occur during and after a collision.