Abstract
We prove, outside the influence region of a ball of radius R 0 centred in the origin of the initial data hypersurface, Σ0, the existence of global solutions near to Kerr spacetime, provided that the initial data are sufficiently near to those of Kerr. This external region is the “far” part of the outer region of the perturbed Kerr spacetime. Moreover, if we assume that the corrections to the Kerr metric decay sufficiently fast, o(r −3), we prove that the various null components of the Riemann tensor decay in agreement with the “Peeling theorem”.
Article PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Avoid common mistakes on your manuscript.
References
Blue P.: Decay of the Maxwell field on the Schwarzschild manifold. J. Hyperbolic Differ. Equ. 5(4), 807–856 (2008)
Chandrasekhar S.: The Mathematical Theory of Black Holes. Oxford University Press, Oxford (1983)
Caciotta G., Nicolò F.: Global characteristic problem for Einstein vacuum equations with small initial data. Part I: the initial data constraints. JHDE 2(1), 201–277 (2005)
Caciotta, G., Nicolò, F.: Global characteristic problem for Einstein vacuum equations with small initial data II. arXiv-gr-qc/0608038 (2006)
Caciotta, G., Nicolò, F.: The non linear perturbation of the Kerr spacetime in an external region. arXiv-gr-qc/0908.4330v1 (2009)
Christodoulou, D., Klainerman, S.: The global non linear stability of the Minkowski space. In: Princeton Mathematical Series, vol. 41 (1993)
Dafermos, M., Rodnianski, I.: A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds. arXiv-0805.4309v1 (2008)
Israel W., Pretorius F.: Quasi-spherical light cones of the Kerr geometry. Class. Quantum Gravity 15, 2289–2301 (1998)
Klainerman, S.: Linear stability of black holes following M. Dafermos and I. Rodnianski. Bourbaki Seminar (2009)
Klainerman, S., Nicolò, F.: The evolution problem in general relativity. In: Progress in Mathematical Physics, vol. 25. Birkhäuser, Boston (2002)
Klainerman S., Nicolò F.: Peeling proerties of asymptotically flat solutions to the Einstein vacuum equation. Class. Quantum Gravity 20, 3215–3257 (2003)
Kroon J.A.V.: Logarithmic Newman-Penrose constants for arbitrary polyhomogeneous spacetime. Class. Quantum Gravity 16, 1653–1665 (1999)
Kroon J.A.V.: Polyhomogeneity and zero rest mass fields with applications to Newman-Penrose constants. Class. Quantum Gravity 17, 605–621 (2000)
Nicolò F.: Canonical foliation on a null hypersurface. JHDE 1(3), 367–427 (2004)
Nicolò, F.: The peeling in the “very external region” of non linear perturbations of the Kerr spacetime. ArXiv gr-qc:0901.3316
Wald R.M.: General Relativity. University of Chicago Press, Chicago (1984)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Piotr T. Chrusciel.
Rights and permissions
About this article
Cite this article
Caciotta, G., Nicolò, F. Non Linear Perturbations of Kerr Spacetime in External Regions and the Peeling Decay. Ann. Henri Poincaré 11, 433–497 (2010). https://doi.org/10.1007/s00023-010-0032-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00023-010-0032-9