Annales Henri Poincaré

, Volume 10, Issue 8, pp 1437–1486 | Cite as

A Gluing Construction Regarding Point Particles in General Relativity

Article
  • 37 Downloads

Abstract

We develop a gluing construction which adds scaled and truncated asymptotically Euclidean solutions of the Einstein constraint equations to compact solutions with potentially non-trivial cosmological constants. The result is a one-parameter family of initial data which has ordinary and scaled “point-particle” limits analogous to those of Gralla and Wald (Class Quantum Grav 25:205009, 2008). In particular, we produce examples of initial data which generalize Schwarzschild–de Sitter initial data and gluing theorems of IMP-type (Isenberg et al. in Comm Math Phys 231:529–568).

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bartnik R., Isenberg J.: Constraint Equations. In: Chruściel, P., Friedrich, H. (eds) The Einstein Equations and Large Scale Behavior of Gravitational Fields, pp. 1–38. Birhäuser, Berlin (2004)Google Scholar
  2. 2.
    Beig R., Chruściel P.T., Schoen R.: KIDs are non-generic. Ann. Henri Poincaré 6(1), 155–194 (2005)MATHCrossRefADSGoogle Scholar
  3. 3.
    Choquet-Bruhat Y.: Théorème d’existence pour certains systèmes d’équations aux dérivées partialles non linéaires. Acta. Math. 88, 141–225 (1952)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Chruściel, P.T., Delay, E.: On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications. Mém. Soc. Math. Fr. (N.S.) 94 (2003)Google Scholar
  5. 5.
    Chruściel P.T., Isenberg J., Pollack D.: Initial data engineering. Comm. Math. Phys. 257(1), 29–42 (2005)MATHCrossRefMathSciNetADSGoogle Scholar
  6. 6.
    Gilbarg D., Trudinger N.S.: Elliptic Partial Differential Equations of the Second Order. Springer, Berlin (1983)Google Scholar
  7. 7.
    Gralla S., Wald R.: A rigorous derivation of gravitational self-force. Class. Quantum Grav. 25, 205009 (2008)CrossRefMathSciNetADSGoogle Scholar
  8. 8.
    Isenberg J., Mazzeo R., Pollack D.: Gluing and wormholes for the Einstein constraint equations. Comm. Math. Phys. 231, 529–568 (2002)MATHCrossRefMathSciNetADSGoogle Scholar
  9. 9.
    Joyce D.: Constant scalar curvature metrics on connected sums. Int. J. Math. Sci. 7, 405–450 (2003)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Lee, J.: Fredholm operators and Einstein metrics on conformally compact manifolds. Mem. Am. Math. Soc. 183 (2006)Google Scholar
  11. 11.
    Moncrief V.: Spacetime symmetries and linearization stability of the Einstein equations I. J. Math. Phys. 16, 493–498 (1975)CrossRefMathSciNetADSGoogle Scholar

Copyright information

© Birkhäuser / Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of Mathematical SciencesLewis & Clark CollegePortlandUSA

Personalised recommendations