Table of Contents
ISRN Geometry
Volume 2011 (2011), Article ID 248615, 9 pages
http://dx.doi.org/10.5402/2011/248615
Research Article

Universality and Constant Scalar Curvature Invariants

1Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, Canada B3H 3J5
2Faculty of Science and Technology, University of Stavanger, 4036 Stavanger, Norway

Received 5 June 2011; Accepted 6 July 2011

Academic Editors: E. H. Saidi and M. Visinescu

Copyright © 2011 A. A. Coley and S. Hervik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. A. Coley, G. W. Gibbons, S. Hervik, and C. N. Pope, “Metrics with vanishing quantum corrections,” Classical and Quantum Gravity, vol. 25, no. 14, Article ID 145017, 17 pages, 2008. View at Publisher · View at Google Scholar
  2. G. W. Gibbons and C. N. Pope, “Time-dependent multi-centre solutions from new metrics with holonomy Sim(n−2),” Classical and Quantum Gravity, vol. 25, no. 12, 2008. View at Publisher · View at Google Scholar
  3. A. Coley, S. Hervik, and N. Pelavas, “Lorentzian spacetimes with constant curvature invariants in three dimensions,” Classical and Quantum Gravity, vol. 25, no. 2, Article ID 025008, 2008. View at Publisher · View at Google Scholar
  4. A. Coley, S. Hervik, and N. Pelavas, “On spacetimes with constant scalar invariants,” Classical and Quantum Gravity, vol. 23, no. 9, pp. 3053–3074, 2006. View at Publisher · View at Google Scholar
  5. A. Coley, S. Hervik, and N. Pelavas, “Lorentzian spacetimes with constant curvature invariants in four dimensions,” Classical and Quantum Gravity, vol. 26, no. 12, Article ID 125011, 17 pages, 2009. View at Publisher · View at Google Scholar
  6. S. A. Fulling, R. C. King, B. G. Wybourne, and C. J. Cummins, “Normal forms for tensor polynomials. I. The Riemann tensor,” Classical and Quantum Gravity, vol. 9, no. 5, pp. 1151–1197, 1992. View at Publisher · View at Google Scholar
  7. Y. Décanini and A. Folacci, “FKWC-bases and geometrical identities for classical and quantum field theories in curved spacetime,” http://arxiv.org/abs/0805.1595.
  8. Y. Décanini and A. Folacci, “Irreducible forms for the metric variations of the action terms of sixth-order gravity and approximated stress-energy tensor,” Classical and Quantum Gravity, vol. 24, no. 18, pp. 4777–4799, 2007. View at Publisher · View at Google Scholar
  9. D. D. Bleecker, “Critical Riemannian manifolds,” Journal of Differential Geometry, vol. 14, no. 4, pp. 599–608, 1979. View at Google Scholar
  10. A. Coley, S. Hervik, and N. Pelavas, “Spacetimes characterized by their scalar curvature invariants,” Classical and Quantum Gravity, vol. 26, no. 2, Article ID 025013, 33 pages, 2009. View at Publisher · View at Google Scholar
  11. D. G. Ebin, “The manifold of Riemannian metrics,” in Proceedings of Symposia in Pure Mathematics, vol. 15, pp. 11–40, Berkeley, Calif, USA, 1968.
  12. J. Isenberg and J. E. Marsden, “A slice theorem for the space of solutions of Einstein's equations,” Physics Reports, vol. 89, no. 2, pp. 179–222, 1982. View at Publisher · View at Google Scholar
  13. A. Coley, A. Fuster, and S. Hervik, “Supergravity solutions with constant scalar invariants,” International Journal of Modern Physics A, vol. 24, no. 6, pp. 1119–1133, 2009. View at Publisher · View at Google Scholar
  14. A. A. Coley, “A class of exact classical solutions to string theory,” Physical Review Letters, vol. 89, no. 28, Article ID 281601, 3 pages, 2002. View at Publisher · View at Google Scholar
  15. A. Coley, “Classification of the Weyl tensor in higher dimensions and applications,” Classical and Quantum Gravity, vol. 25, no. 3, Article ID 033001, 29 pages, 2008. View at Publisher · View at Google Scholar