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Fixed mesh refinement in the characteristic formulation of general relativity

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Abstract

We implement a spatially fixed mesh refinement under spherical symmetry for the characteristic formulation of General Relativity. The Courant–Friedrich–Levy condition lets us deploy an adaptive resolution in (retarded-like) time, even for the nonlinear regime. As test cases, we replicate the main features of the gravitational critical behavior and the spacetime structure at null infinity using the Bondi mass and the News function. Additionally, we obtain the global energy conservation for an extreme situation, i.e. in the threshold of the black hole formation. In principle, the calibrated code can be used in conjunction with an ADM 3+1 code to confirm the critical behavior recently reported in the gravitational collapse of a massless scalar field in an asymptotic anti-de Sitter spacetime. For the scenarios studied, the fixed mesh refinement offers improved runtime and results comparable to code without mesh refinement.

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Acknowledgements

The authors thank the financial support of the Brazilian agencies Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ). H. P. O. thanks FAPERJ for support within the Grant No. E-26/202.998/2016 Bolsas de Bancada de Projetos (BBP).

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Authors and Affiliations

  1. Facultad de Ciencias, Centro de Física Fundamental, Universidad de Los Andes, Mérida, Venezuela

    W. Barreto

  2. Departamento de Física Teórica, Instituto de Física A. D. Tavares, Universidade do Estado do Rio de Janeiro, R. São Francisco Xavier, 524, Rio de Janeiro, 20550-013, RJ, Brasil

    W. Barreto & H. P. de Oliveira

  3. Computational Science Research Center, San Diego State University, San Diego, CA, USA

    B. Rodriguez-Mueller

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  1. W. Barreto
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  2. H. P. de Oliveira
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  3. B. Rodriguez-Mueller
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Correspondence to W. Barreto.

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Barreto, W., de Oliveira, H.P. & Rodriguez-Mueller, B. Fixed mesh refinement in the characteristic formulation of general relativity. Gen Relativ Gravit 49, 107 (2017). https://doi.org/10.1007/s10714-017-2273-0

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  • DOI: https://doi.org/10.1007/s10714-017-2273-0

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