Numerical Evolution of 5D Asymptotically AdS Spacetimes

          @misc{ pirsa_PIRSA:12040109,
            doi = {10.48660/12040109},
            url = {https://pirsa.org/12040109},
            author = {Pretorius, Frans},
            keywords = {},
            language = {en},
            title = {Numerical Evolution of 5D Asymptotically AdS Spacetimes},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {apr},
            note = {PIRSA:12040109 see, \url{https://pirsa.org}}
          }
          

Abstract

I will describe a new numerical effort to solve Einstein gravity in 5-dimensional asymptotically Anti de Sitter spacetimes (AdS). The motivation is the gauge/gravity duality of string theory, with application to scenarios that on the gravity side are described by dynamical, strong-field solutions. For example, it has been argued that certain properties of the quark-gluon plasma formed in heavy-ion collisions can be modeled by a conformal field theory, with the dual description on the gravity side provided by the collision of black holes. As a first step towards modeling such more general phenomena, we initially focus on spacetimes with SO(3) symmetry in the bulk; i.e., axisymmetric gravity, dual to states with spherical or special conformal symmetry on the boundary. For a first application we study quasi-normal ringdown of highly deformed black holes in the bulk. Even though the initial states are far from equilibrium, the boundary state is remarkably well described as a hydrodynamic flow from early times. The code is based on the generalized harmonic formulation of the field equations, and though this method has been shown to work well in many asymptotically flat scenarios, there are unique challenges that arise in obtaining regular, stable solutions in asymptotically AdS spacetimes. I will describe these challenges, and the way we have addressed them.