Global Regularity for the 2+1 Dimensional Equivariant Einstein-Wave Map System

被引：2

作者：

Andersson L. ^{[1
]}

Gudapati N. ^{[2
]}

Szeftel J. ^{[3
]}

机构：

[1] Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam

[2] Department of Mathematics, Yale University, New Haven, CT

[3] Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

来源：

Annals of PDE | / 3卷 / 2期

基金：

美国国家科学基金会;

关键词：

Einstein’s equations; Wave maps;

D O I：

10.1007/s40818-017-0030-z

中图分类号：

学科分类号：

摘要：

In this paper we consider the equivariant 2+1 dimensional Einstein-wave map system and show that if the target satisfies the so called Grillakis condition, then global existence holds. In view of the fact that the 3+1 vacuum Einstein equations with a spacelike translational Killing field reduce to a 2+1 dimensional Einstein-wave map system with target the hyperbolic plane, which in particular satisfies the Grillakis condition, this work proves global existence for the equivariant class of such spacetimes. © 2017, Springer International Publishing AG.

引用

共 36 条

[1]

Andersson L., The global existence problem in general relativity, Gen. Relativ. Quantum Cosmol, (1999)

[2]

Andersson L., The global existence problem in general relativity, The Einstein Equations and the Large Scale Behavior of Gravitational Fields, pp. 71-120, (2004)

[3]

Ashtekar A., Varadarajan M., Striking property of the gravitational Hamiltonian, Phys. Rev. D (3), 50, 8, pp. 4944-4956, (1994)

[4]

Beem J.K., Ehrlich P.E., Easley K.L., Global Lorentzian Geometry, Volume 202 of Monographs and Textbooks in Pure and Applied Mathematics, (1996)

[5]

Berger B.K., Chrisciel P., Moncrief V., On “asymptotically flat” space-times with G-2 invariant Cauchy surfaces, Ann. Phys., 237, pp. 322-354, (1995)

[6]

Bernal A.N., Sanchez M., Further results on the smoothability of Cauchy hypersurfaces and Cauchy time functions, Lett. Math. Phys., 77, pp. 183-197, (2006)

[7]

Carot J., Some developments on axial symmetry, Class. Quantum Gravity, 17, pp. 2675-2690, (2000)

[8]

Choquet-Bruhat Y., Geroch R., Global aspects of the Cauchy problem in general relativity, Commun. Math. Phys., 14, pp. 329-335, (1969)

[9]

Christodoulou D., The instability of naked singularities in the gravitational collapse of a scalar field, Ann. Math. (2), 149, 1, pp. 183-217, (1999)

[10]

Christodoulou D., Tahvildar-Zadeh A.S., On the regularity of spherically symmetric wave maps, Commun. Pure Appl. Math., 46, 7, pp. 1041-1091, (1993)

← 1 2 3 4 →