Zilhão, Miguel and Witek, Helvi and Sperhake, Ulrich and Cardoso, Vitor and Gualtieri, Leonardo and Herdeiro, Carlos and Nerozzi, Andrea (2010) Numerical relativity for D dimensional axially symmetric space-times: Formalism and code tests. Physical Review D, 81 (8). 084052 . ISSN 0556-2821 http://resolver.caltech.edu/CaltechAUTHORS:20100521-152555999
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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 gauge-gravity 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 space-times than those investigated hitherto, by developing a framework to study the numerical evolution of D dimensional vacuum space-times with an SO(D-2) isometry group for D≥5, or SO(D-3) for D≥6. Performing a dimensional reduction on a (D-4) 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. Brill-Lindquist 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 space-times. Specifically, we present a modified moving puncture gauge, which facilitates long-term 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.
|Additional Information:||© 2010 American Physical Society. Received 18 January 2010; published 29 April 2010. We would like to thank L. Lindblom and M. Sampaio for discussions.We also thank the participants of the V Iberian Cosmology Meeting, the XII Marcel Grossmann Meetings, the Spanish Relativity Meeting, and the I and II Black Holes Workshop for useful feedback. M. Z. and H.W. are funded by FCT through Grants No. SFRH/BD/43558/2008 and No. SFRH/BD/46061/2008. V. C. acknowledges financial support from Fundac¸a˜o Calouste Gulbenkian. V. C. and C. H. are supported by a ‘‘Cieˆncia 2007’’ research contract. A. N. is funded by FCT through Grant No. SFRH/BPD/47955/2008. This work was partially supported by FCT–Portugal through Projects No. PTDC/FIS/ 64175/2006, No. PTDC/FIS/098025/2008, No. PTDC/FIS/ 098032/2008 No. PTDC/CTE-AST/098034/2008, No. CERN/FP/109306/2009, and No. CERN/FP/109290/ 2009, as well as NSF Grants No. PHY-090003, No. PHY- 0900735, and the Fairchild foundation to Caltech. Computations were performed on the TeraGrid clusters ranger and kraken and at Magerit in Madrid.|
|Classification Code:||PACS: 04.25.D-, 04.25.dg, 04.50.-h, 04.50.Gh|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Jason Perez|
|Deposited On:||25 May 2010 14:57|
|Last Modified:||26 Dec 2012 12:03|
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