|
On the connectedness of the space of initial data for the Einstein equations
Author(s):
Brian
Smith;
Gilbert
Weinstein
Journal:
Electron. Res. Announc. Amer. Math. Soc.
6
(2000),
52-63.
MSC (2000):
Primary 83C05;
Secondary 58G11
Posted:
July 19, 2000
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
Is the space of initial data for the Einstein vacuum equations connected? As a partial answer to this question, we prove the following result: Let  be the space of asymptotically flat metrics of non-negative scalar curvature on  which admit a global foliation outside a point by  -spheres of positive mean and Gauss curvatures. Then  is connected.
References:
-
- 1.
- R. Bartnik, Existence of maximal surfaces in asymptotically flat spacetimes, Comm. Math. Phys. 94 (1984), no. 2, 155-175. MR 86b:53063
- 2.
- R. Bartnik, Quasispherical metrics and prescribed scalar curvature, J. Differential Geom. 37 (1993), no. 1, 31-71. MR 93i:53041
- 3.
- M. Cantor, A necessary and sufficient condition for York data to specify an asymptotically flat spacetime, J. Math. Phys. 20 1979, 1741-1744. MR 80k:83018
- 4.
- M. Cantor and D. Brill, The Laplacian on asymptotically flat manifolds and the specification of scalar curvature, Comp. Math. 43 (1981), fasc. 3, 317-330. MR 83a:58021
- 5.
- A. Chaljub-Simon and Y. Choquet-Bruhat, Problèmes elliptiques du second ordre sur une variété euclidienne à l'infini, Ann. Fac. Sci. Toulouse Math. 5 (1979), no. 1, 9-25. MR 80i:58044
- 6.
- Y. Choquet-Bruhat, Global solutions of the constraints equations on open and closed manifolds, GRG 5 (1974), no. 1, 49-60. MR 53:10100
- 7.
- Y. Choquet-Bruhat, J. Isenberg, and J. W. York, Jr, Einstein constraints on asymptotically Euclidean manifolds, Phys. Rev. D. 61 (2000), article # 084034.
- 8.
- D. Christodoulou and S. Klainerman, The global nonlinear stabililty of the Minkowski space, Princeton Mathematical Series, No. 41, Princeton University Press, Princeton, 1993. MR 95k:83006
- 9.
- D. Christodoulou and N. O'Murchadha, The boost problem in general relativity, Comm. in Math. Phys. 80 (1981), no. 2, 271-300. MR 84e:83011
- 10.
- A. E. Fischer, J. E. Marsden, and V. Moncrief, The structure of the space of solutions of Einstein's equations. I, One Killing field, Ann. Inst. H. Poincaré Sect. A (N.S.), 33 (1980), no. 2, 147-194. MR 82d:83007
- 11.
- O. A. Ladyzenskaja, V. A. Solonnikov, and N. N. Ural'ceva, Linear and quasilinear equations of parabolic type, Transl. of Math. Mono., Vol. 23, AMS, Providence, RI, 1968. MR 39:3159b
- 12.
- J. M. Lee and T. H. Parker, The Yamabe problem, Bull. Amer. Math. Soc. (N.S.) 17 (1987), no. 1, 37-91. MR 88f:53001
- 13.
- B. Smith and G. Weinstein, Quasiconvex foliations and asymptotically flat metrics of non-negative scalar curvature, in preparation.
- 14.
- R. M. Wald, General relativity, The University of Chicago Press, Chicago, IL, 1984. MR 86a:83001
- 15.
- J. W. York, Jr., Gravitational degrees of freedom and the initial-value problem, Phys. Rev. Lett. 23 (1971), no. 26, 1656-1658. MR 44:7944
Similar Articles:
Retrieve articles in Electronic Research Announcements
with MSC
(2000):
83C05,
58G11
Retrieve articles in all Journals with MSC
(2000):
83C05,
58G11
Additional Information:
Brian
Smith
Affiliation:
University of Alabama at Birmingham, Birmingham, AL 35205
Email:
smith@math.uab.edu
Gilbert
Weinstein
Affiliation:
University of Alabama at Birmingham, Birmingham, AL 35205
Email:
weinstei@math.uab.edu
DOI:
10.1090/S1079-6762-00-00081-0
PII:
S 1079-6762(00)00081-0
Received by editor(s):
May 27, 1999
Posted:
July 19, 2000
Additional Notes:
This research was supported in part by NSF grant DMS~9704760.
Communicated by:
Richard Schoen
Copyright of article:
Copyright
2000,
American Mathematical Society
|
Comments: webmaster@ams.org