# Simulation of asymptotically AdS(5) spacetimes with a generalized harmonic evolution scheme

## Author(s): Bantilan, Hans; Pretorius, Frans; Gubser, Steven S

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 Abstract: Motivated by the gauge/gravity duality, we introduce a numerical scheme based on generalized harmonic evolution to solve the Einstein field equations on asymptotically anti-de Sitter spacetimes. We work in global AdS(5), which can be described by the (t, r, chi, theta, phi) spherical coordinates adapted to the R x S-3 boundary. We focus on solutions that preserve an SO(3) symmetry that acts to rotate the 2-spheres parametrized by theta, phi. In the boundary conformal field theory, the way in which this symmetry manifests itself hinges on the way we choose to embed Minkowski space in R x S-3. We present results from an ongoing study of prompt black hole formation via scalar field collapse, and explore the subsequent quasinormal ringdown. Beginning with initial data characterized by highly distorted apparent horizon geometries, the metrics quickly evolve, via quasinormal ringdown, to equilibrium static black hole solutions at late times. The lowest angular number quasinormal modes are consistent with the linear modes previously found in perturbative studies, whereas the higher angular modes are a combination of linear modes and of harmonics arising from nonlinear mode coupling. We extract the stress energy tensor of the dual conformal field theory on the boundary, and find that despite being highly inhomogeneous initially, it nevertheless evolves from the outset in a manner that is consistent with a thermalized N = 4 SYM fluid. As a first step towards closer contact with relativistic heavy ion collision physics, we map this solution to a Minkowski piece of the R x S-3 boundary, and obtain a corresponding fluid flow in Minkowski space. Publication Date: 15-Apr-2012 Electronic Publication Date: 26-Apr-2012 Citation: Bantilan, Hans, Pretorius, Frans, Gubser, Steven S. (2012). Simulation of asymptotically AdS(5) spacetimes with a generalized harmonic evolution scheme. PHYSICAL REVIEW D, 85 (10.1103/PhysRevD.85.084038 DOI: doi:10.1103/PhysRevD.85.084038 ISSN: 2470-0010 EISSN: 2470-0029 Type of Material: Journal Article Journal/Proceeding Title: PHYSICAL REVIEW D Version: Final published version. This is an open access article.