On local equivalence problem of space-times with two orthogonally transitive commuting Killing fields
Considered is the problem of local equivalence of generic four-dimensional metrics possessing two commuting and orthogonally transitive Killing vector fields. A sufficient set of eight differential in...
Considered is the problem of local equivalence of generic four-dimensional metrics possessing two commuting and orthogonally transitive Killing vector fields. A sufficient set of eight differential in...
Differential Galois obstructions for integrability of homogeneous Newton equations
In this paper, we formulate necessary conditions for the integrability in the Jacobi sense of Newton equations =−F(q), where qn and all components of F are polynomial and homogeneous of the same...
In this paper, we formulate necessary conditions for the integrability in the Jacobi sense of Newton equations =−F(q), where qn and all components of F are polynomial and homogeneous of the same...
Positive mass theorems for higher dimensional Lorentzian manifolds
J. Math. Phys. 49, 022504 (2008); doi:10.1063/1.2830803
Published 6 February 2008
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We extend Witten's proof [“A new proof of the positive energy theorem,” Commun. Math. Phys. 80, 381–402 (1981)] of the positive mass theorem to a rigorous proof for Lorentzian manifolds of any dimension. This includes the original higher-dimensional positive mass theorem proved by spinors [Parker, T. and Taubes, C., “On Witten's proof of the positive energy theorem,” Commun. Math. Phys. 84, 223–238 (1982)] for dimension 4 and [Zhang, X., “Positive mass conjecture for five-dimensional Lorentzian manifolds,” J. Math. Phys. 40, 3540–3552 (1999)] for dimension 5. Stimulated by the article of Zhang [“Positive mass theorem for hypersurface in 5-dimensional Lorentzian manifolds,” Commun. Anal. Geom. 8, 635–652 (2000)], we weaken the spin condition on the spacelike hypersurface to require only a spinc structure and give a modified positive mass theorem for Lorentzian manifolds for dimensions 4, 5, and 6.
©2008 American Institute of Physics
| History: | Received 3 April 2007; accepted 10 December 2007; published 6 February 2008 |
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http://link.aip.org/link/?JMAPAQ/49/022504/1 |
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REFERENCES (15)
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- Arnowitt, S., Deser, S., and Misner, C., “Coordinate invariance and energy expressions in general relativity,” Phys. Rev. 122, 997–1006 (1961).
- Bartnik, R., “The mass of an asymptotically flat manifold,”
Commun. Pure Appl. Math. 36, 661–693 (1986) . - Baum, H., A remark on the spectrum of the Dirac operator on pseudo-Riemannian spin manifolds (http://www-irm.mathematik.hu-berlin.de/~baum/publikationen-fr/publikationen.htm).
- Dai, X., “A Positive Mass Theorem for spaces with asymptotic SUSY compactification,”
Commun. Math. Phys. 244, 335–345 (2004) . - Dai, X., “A note on positive energy theorem for spaces with asymptotic SUSY compactification,” J. Math. Phys. 46, 042505 (2005).
- Hawking, S., and Ellis, S., The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973).
- Lu, Q. K., and Wu, K., “A representation of the Lorentzian spin group and its application,” Acta Math. Appl. Sin. 23, 577–598 (2007).
- Parker, T., and Taubes, C., “On Witten's proof of the positive energy theorem,”
Commun. Math. Phys. 84, 223–238 (1982) . - Schoen, R., and Yau, S. T., “On the proof of the positive mass conjecture in general relativity,”
Commun. Math. Phys. 65, 45–76 (1979) . - Schoen, R., and Yau, S. T., “The energy and the linear momentum of space-times in general relativity,”
Commun. Math. Phys. 79, 47–51 (1981) . - Schoen, R., and Yau, S. T., “Proof of the positive mass theorem. II,”
Commun. Math. Phys. 79, 231–260 (1981) . - Witten, E., “A new proof of the positive energy theorem,”
Commun. Math. Phys. 80, 381–402 (1981) . - Xie, N. Q., “A generalized positive energy theorem for spaces with asymptotic SUSY compactification,”
J. Geom. Phys. 56, 271–281 (2006) . - Zhang, X., “Positive mass conjecture for five-dimensional Lorentzian manifolds,” J. Math. Phys. 40, 3540–3552 (1999).
- Zhang, X., “Positive mass theorem for hypersurface in 5-dimensional Lorentzian Manifolds,”
Commun. Anal. Geom. 8, 635–652 (2000) .
