2012/01/31 by H. Bantilan, Hans Bantilan, Frans Pretorius +1 · 95 citations
Mathematics · Physics and Astronomy · #Anti-de Sitter space #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Boundary (topology) #Cosmology and Gravitation Theories #Geodesic #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Physics #Quantum mechanics #Spherical harmonics #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.85.084038
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 85(8) (American Physical Society)
arxiv created 2012/04/09 · openalex publication_date 2012/04/26 · arxiv updated 2013/05/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 AdS5, which can be described by the (t, r, \ensuremathχ, \ensuremathθ, \ensuremathφ) spherical coordinates adapted to the ℝ\ifmmode×\else\texttimes\fiS3 boundary. We focus on solutions that preserve an SO(3) symmetry that acts to rotate the 2-spheres parametrized by \ensuremathθ, \ensuremathφ. 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\ifmmode×\else\texttimes\fiS3. 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\ifmmode×\else\texttimes\fiS3 boundary, and obtain a corresponding fluid flow in Minkowski space.