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Numerical integration of Einstein’s field equations
Open accessAbstract
Many numerical codes now under development to solve Einstein's equations of general relativity in $(3+1)$-dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial metric and extrinsic curvature tensors. Following Shibata and Nakamura, we modify these equations by factoring out the conformal factor and introducing three ``connection functions.'' The evolution equations can then be reduced to wave equations for the conformal metric components, which are coupled to evolution equations for the connection functions. We evolve small amplitude gravitational waves and make a direct comparison of the numerical performance of the modified equations with the standard ADM equations. We find that the modified form exhibits much improved stability.
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Cites
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Boosted Three-Dimensional Black-Hole Evolutions with Singularity Excision
Cook, G. B., Huq, M. F., Klasky, S., Scheel, M., Abrahams, A. M., Anderson, A., Anninos, P., Baumgarte, T. W., Bishop, N. T., Brandt, S. R., et al. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2512 · Cited by 114
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Cited by
Stergioulas, N. (2003) · Living Reviews in Relativity · doi:10.12942/lrr-2003-3 · Cited by 554
Maximum Kick from Nonspinning Black-Hole Binary Inspiral
González, J. A., Sperhake, U., Brügmann, B., Hannam, M., & Husa, S. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.091101 · Cited by 477
Liebling, S. L., & Palenzuela, C. (2017) · Living Reviews in Relativity · doi:10.1007/s41114-017-0007-y · Cited by 371
Matter effects on binary neutron star waveforms
Read, J. S., Baiotti, L., Creighton, J. D. E., Friedman, J. L., Giacomazzo, B., Kyutoku, K., Markakis, C., Rezzolla, L., Shibata, M., & Taniguchi, K. (2013) · Physical Review D · doi:10.1103/physrevd.88.044042 · Cited by 320
Metadata
- Authors
- Baumgarte, T. W., & Shapiro, S. L.
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 1998-12-07
- Volume
- 59
- Issue
- 2
- ISSN
- 0556-2821 (ISSN-L)
- 1089-4918
- OpenAlex
- W2104853465
- Cited by
- 1,248
- References
- 13
- FWCI
- 11.54
- Type
- journal article
- Language
- en
- Open access
- green
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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