Numerical relativity for D dimensional axially symmetric spacetimes: Formalism and code tests
Abstract
The numerical evolution of Einstein’s field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gaugegravity duality, to modeling black hole production in TeV gravity scenarios, to analysis of the stability of exact solutions, and to tests of cosmic censorship. In order to investigate these questions, we extend numerical relativity to more general spacetimes than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum spacetimes with an SO(D2) isometry group for D≥5, or SO(D3) for D≥6. Performing a dimensional reduction on a (D4) sphere, the D dimensional vacuum Einstein equations are rewritten as a 3+1 dimensional system with source terms, and presented in the Baumgarte, Shapiro, Shibata, and Nakamura formulation. This allows the use of existing 3+1 dimensional numerical codes with small adaptations. BrillLindquist initial data are constructed in D dimensions and a procedure to match them to our 3+1 dimensional evolution equations is given. We have implemented our framework by adapting the Lean code and perform a variety of simulations of nonspinning black hole spacetimes. Specifically, we present a modified moving puncture gauge, which facilitates longterm stable simulations in D=5. We further demonstrate the internal consistency of the code by studying convergence and comparing numerical versus analytic results in the case of geodesic slicing for D=5, 6.
 Publication:

Physical Review D
 Pub Date:
 April 2010
 DOI:
 10.1103/PhysRevD.81.084052
 arXiv:
 arXiv:1001.2302
 Bibcode:
 2010PhRvD..81h4052Z
 Keywords:

 04.25.D;
 04.25.dg;
 04.50.h;
 04.50.Gh;
 Numerical relativity;
 Numerical studies of black holes and blackhole binaries;
 Higherdimensional gravity and other theories of gravity;
 Higherdimensional black holes black strings and related objects;
 General Relativity and Quantum Cosmology;
 Astrophysics  High Energy Astrophysical Phenomena;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 31 pages, 6 figures