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We present a symmetric hyperbolic formulation of the Einstein equations in affine-null coordinates.
J. Winicour, Living Rev. Rel. 12
1903
Earlier work this paper cites.
D. Hilditch, J. A. Valiente Kroon, and P. Zhao, Gen. Rel. Grav. 52
1911
Earlier work this paper cites.
H. Bondi, Nature 186
1960
Earlier work this paper cites.
R. K. . Sachs and H. Bondi, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 270
1962
Earlier work this paper cites.
H. Bondi, M. G. J. Van der Burg, and A. W. K. Metzner, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 269
1962
Earlier work this paper cites.
E. Newman and R. Penrose, Journal of Mathematical Physics 3
1962
Earlier work this paper cites.
L. A. Tamburino and J. H. Winicour, Phys. Rev. 150
1966
Earlier work this paper cites.
R. Geroch, A. Held, and R. Penrose, Journal of Mathematical Physics 14
1973
Earlier work this paper cites.
H. Friedrich, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 375
1981
Cited alongside, same era.
H. Kreiss and J. Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations , ISSN (Elsevier Science, 1989)
1989
Cited alongside, same era.
A. D. Rendall, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 427
1990
Cited alongside, same era.
B. Gustafsson, H. Kreiss, and J. Oliger, Time Dependent Problems and Difference Methods , A Wiley-Interscience Publication (Wiley, 1995)
1995
Cited alongside, same era.
N. T. Bishop, R. Gomez, L. Lehner, and J. Winicour, Phys. Rev. D 54
1996
Cited alongside, same era.
O. Brodbeck, S. Frittelli, P. Hübner, and O. A. Reula, Journal of Mathematical Physics 40
C. Gundlach, J. M. Martin-Garcia, G. Calabrese, and I. Hinder, Class. Quant. Grav. 22
2005
Later among the works it cites.
T. Giannakopoulos, D. Hilditch, and M. Zilhao, Phys. Rev. D 102
2007
Later among the works it cites.
J. Luk, (2011), arXiv:1107.0898 [gr-qc]
2011
Later among the works it cites.
O. Sarbach and M. Tiglio, Living Rev. Rel. 15
2012
Later among the works it cites.
D. Hilditch, Int. J. Mod. Phys. A 28
2012
Later among the works it cites.
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1999
Cited alongside, same era.
S. Chandrasekhar, The mathematical theory of black holes , Oxford classic texts in the physical sciences (Oxford Univ. Press, Oxford, 2002)
2002
Cited alongside, same era.
We note that the possibility of a strongly hyperbolic formulation of the Einstein equations for Bondi-like coordinate systems existing for a tetrad-based formalism was suggested by Giannakopoulos et. al. [ 9 ]
Cited in the paper.
As is stressed in [ 9 ] though, this does not imply that a numerical solution of a weakly hyperbolic system will necessarily exhibit any pathological behavior at a given fixed resolution
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For a review which discusses earlier attempts to formulate a well-posed initial value problem for single-null formulations of the Einstein equations, see [ 7 ]
Cited in the paper.
For example, this is done in [ 12 ] . In their case it is more straightforward to do this as with their tetrad condition the δ \delta derivatives only involve “angular” derivatives, so the Newman-Penrose equations ( 33k
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2014
Later among the works it cites.
C. J. Handmer, B. Szilágyi, and J. Winicour, Class. Quant. Grav. 33
2016
Later among the works it cites.