Y. Choquet-Bruhat, P. T. Chruściel, and J. Loizelet :
“Global solutions of the Einstein–Maxwell equations in higher dimensions Classical Quantum Gravity
23 : 24
(2006 ),
pp. 7383–7394 .
MR
2279722 Zbl
1117.83024 article
Abstract
People
BibTeX
We consider the Einstein–Maxwell equations in space-dimension \( n \) . We point out that the Lindblad–Rodnianski stability proof applies to those equations whatever the space-dimension \( n \geq 3 \) . In even spacetime dimension \( n + 1 \geq 6 \) , we use the standard conformal method on a Minkowski background to give a simple proof that the maximal globally hyperbolic development of initial data sets which are sufficiently close to the data for Minkowski spacetime and which are Schwarzschildian outside of a compact set lead to geodesically complete spacetimes, with a complete Scri, with a smooth conformal structure, and with the gravitational field approaching the Minkowski metric along null directions at least as fast as \( r^{-(n-1)/2} \) .
@article {key2279722m,
AUTHOR = {Choquet-Bruhat, Yvonne and Chru\'{s}ciel,
Piotr T. and Loizelet, Julien},
TITLE = {Global solutions of the {E}instein--{M}axwell
equations in higher dimensions},
JOURNAL = {Classical Quantum Gravity},
FJOURNAL = {Classical and Quantum Gravity},
VOLUME = {23},
NUMBER = {24},
YEAR = {2006},
PAGES = {7383--7394},
DOI = {10.1088/0264-9381/23/24/011},
NOTE = {MR:2279722. Zbl:1117.83024.},
ISSN = {0264-9381},
}
Y. Choquet-Bruhat, P. T. Chruściel, and J. M. Martín-García :
“The light-cone theorem Classical Quantum Gravity
26 : 13
(2009 ),
pp. 135011, 22 .
MR
2515694 Zbl
1171.83001 article
Abstract
People
BibTeX
We prove that the area of cross-sections of light cones, in spacetimes satisfying suitable energy conditions, is smaller than or equal to that of the corresponding cross-sections in Minkowski, or de Sitter, or anti-de Sitter spacetime. The equality holds if and only if the metric coincides with the corresponding model in the domain of dependence of the light cone.
@article {key2515694m,
AUTHOR = {Choquet-Bruhat, Yvonne and Chru\'{s}ciel,
Piotr T. and Mart\'{\i}n-Garc\'{\i}a,
Jos\'{e} M.},
TITLE = {The light-cone theorem},
JOURNAL = {Classical Quantum Gravity},
FJOURNAL = {Classical and Quantum Gravity},
VOLUME = {26},
NUMBER = {13},
YEAR = {2009},
PAGES = {135011, 22},
DOI = {10.1088/0264-9381/26/13/135011},
NOTE = {MR:2515694. Zbl:1171.83001.},
ISSN = {0264-9381},
}
Y. Choquet-Bruhat, P. T. Chruściel, and J. M. Martín-García :
“A property of light-cones in Einstein’s gravity C. R. Math. Acad. Sci. Paris
347 : 15–16
(2009 ),
pp. 971–977 .
MR
2542904 Zbl
1170.83005 article
Abstract
People
BibTeX
We prove that the area of cross-sections of future light-cones in a space-time of arbitrary dimension, solution of the Einstein equations with sources satisfying suitable energy conditions, is smaller than the area of corresponding cross-sections for Minkowskian cones, equal only in space-times which are Minkowskian to the future of the light-cone.
@article {key2542904m,
AUTHOR = {Choquet-Bruhat, Yvonne and Chru\'{s}ciel,
Piotr T. and Mart\'{\i}n-Garc\'{\i}a,
Jos\'{e} M.},
TITLE = {A property of light-cones in {E}instein's
gravity},
JOURNAL = {C. R. Math. Acad. Sci. Paris},
FJOURNAL = {Comptes Rendus Math\'{e}matique. Acad\'{e}mie
des Sciences. Paris},
VOLUME = {347},
NUMBER = {15-16},
YEAR = {2009},
PAGES = {971--977},
DOI = {10.1016/j.crma.2009.06.001},
NOTE = {MR:2542904. Zbl:1170.83005.},
ISSN = {1631-073X},
}
Y. Choquet-Bruhat, P. T. Chruściel, and J. M. Martín-García :
“Einstein constraints on a characteristic cone 93–102
in
Proceedings “WASCOM 2009” 15th Conference on Waves and Stability in Continuous Media .
World Sci. Publ. (Hackensack, NJ ),
2010 .
MR
2762005 Zbl
1243.83015 inproceedings
Abstract
People
BibTeX
We analyse the Cauchy problem on a characteristic cone, including its vertex, for the Einstein equations in arbitrary dimensions. We use a wave map gauge, solve the obtained constraints and show gauge conservation.
@inproceedings {key2762005m,
AUTHOR = {Choquet-Bruhat, Y. and Chru\'{s}ciel,
P. T. and Mart\'{\i}n-Garc\'{\i}a, J.
M.},
TITLE = {Einstein constraints on a characteristic
cone},
BOOKTITLE = {Proceedings ``{WASCOM} 2009'' 15th {C}onference
on {W}aves and {S}tability in {C}ontinuous
{M}edia},
PUBLISHER = {World Sci. Publ.},
ADDRESS = {Hackensack, NJ},
YEAR = {2010},
PAGES = {93--102},
DOI = {10.1142/9789814317429_0016},
NOTE = {MR:2762005. Zbl:1243.83015.},
}
Y. Choquet-Bruhat, P. T. Chruściel, and J. M. Martín-García :
“The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions Ann. Henri Poincaré
12 : 3
(2011 ),
pp. 419–482 .
MR
2785136 Zbl
1215.83016 article
Abstract
People
BibTeX
We derive explicit formulae for a set of constraints for the Einstein equations on a null hypersurface, in arbitrary space-time dimensions \( n + 1 \geq 3 \) . We solve these constraints and show that they provide necessary and sufficient conditions so that a spacetime solution of the Cauchy problem on a characteristic cone for the hyperbolic system of the reduced Einstein equations in wave-map gauge also satisfies the full Einstein equations. We prove a geometric uniqueness theorem for this Cauchy problem in the vacuum case.
@article {key2785136m,
AUTHOR = {Choquet-Bruhat, Yvonne and Chru\'{s}ciel,
Piotr T. and Mart\'{\i}n-Garc\'{\i}a,
Jos\'{e} M.},
TITLE = {The {C}auchy problem on a characteristic
cone for the {E}instein equations in
arbitrary dimensions},
JOURNAL = {Ann. Henri Poincar\'{e}},
FJOURNAL = {Annales Henri Poincar\'{e}. A Journal
of Theoretical and Mathematical Physics},
VOLUME = {12},
NUMBER = {3},
YEAR = {2011},
PAGES = {419--482},
DOI = {10.1007/s00023-011-0076-5},
NOTE = {MR:2785136. Zbl:1215.83016.},
ISSN = {1424-0637},
}
Y. Choquet-Bruhat, P. T. Chruściel, and J. M. Martín-García :
“An existence theorem for the Cauchy problem on a characteristic cone for the Einstein equations 73–81
in
Complex analysis and dynamical systems, IV: Part 2 .
Edited by M. Agranovsky, M. Ben-Artzi, G. Galloway, L. Karp, S. Reich, D. S. G. Weinstein, and L. Zalcman .
Contemp. Math. 554 .
American Mathematical Society; Bar-Ilan University (Providence, RI; Ramat Gan ),
2011 .
MR
2884395 Zbl
1235.83011 incollection
Abstract
People
BibTeX
@incollection {key2884395m,
AUTHOR = {Choquet-Bruhat, Y. and Chru\'{s}ciel,
Piotr T. and Mart\'{\i}n-Garc\'{\i}a,
Jos\'{e} M.},
TITLE = {An existence theorem for the {C}auchy
problem on a characteristic cone for
the {E}instein equations},
BOOKTITLE = {Complex analysis and dynamical systems,
{IV}: {P}art 2},
EDITOR = {Mark Agranovsky and Matania Ben-Artzi
and Greg Galloway and Lavi Karp and
Simeon Reich and David Shoikhet Gilbert
Weinstein and Lawrence Zalcman},
SERIES = {Contemp. Math.},
NUMBER = {554},
PUBLISHER = {American Mathematical Society; Bar-Ilan
University},
ADDRESS = {Providence, RI; Ramat Gan},
YEAR = {2011},
PAGES = {73--81},
DOI = {10.1090/conm/554/10961},
NOTE = {MR:2884395. Zbl:1235.83011.},
}
Y. Choquet-Bruhat, P. T. Chruściel, and J. M. Martín-García :
“An existence theorem for the Cauchy problem on the light-cone for the vacuum Einstein equations with near-round analytic data ,”
Uch. Zap. Kazan. Univ. Ser. Fiz.-Mat. Nauki
153 : 3
(2011 ),
pp. 115–138 .
MR
3244416 Zbl
1344.83002 article
Abstract
People
BibTeX
@article {key3244416m,
AUTHOR = {Choquet-Bruhat, Y. and Chru\'{s}ciel,
P. T. and Mart\'{\i}n-Garc\'{\i}a, J.
M.},
TITLE = {An existence theorem for the {C}auchy
problem on the light-cone for the vacuum
{E}instein equations with near-round
analytic data},
JOURNAL = {Uch. Zap. Kazan. Univ. Ser. Fiz.-Mat.
Nauki},
FJOURNAL = {Uchenye Zapiski Kazanskogo Universiteta.
Seriya Fiziko-Matematicheskie Nauki},
VOLUME = {153},
NUMBER = {3},
YEAR = {2011},
PAGES = {115--138},
NOTE = {MR:3244416. Zbl:1344.83002.},
ISSN = {2541-7746},
}
