Abstract
I describe the construction of a large class of asymptotically flat initial data with non-vanishing mass and angular momentum for which the metric and the extrinsic curvature have asymptotic expansions at space-like infinity in terms of powers of a radial coordinate. I emphasize the motivations and the main ideas behind the proofs.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
L. Andersson and P. Chruściel. On hyperboloidal Cauchy data for vacuum Einstein equations and obstructions to the smoothness of scri. Commun. Math. Phys., 161, 533–568, 1994.
L. Andersson, P. Chruściel, and H. Friedrich. On the regularity of solutions to the Yamabe equation and the existence of smooth hyperboloidal initial data for Einstein’s field equations. Commun. Math. Phys., 149, 587–612, 1992.
J. Baker and R. Puzio. A new method for solving the initial value problem with application to multiple black holes. Phys. Rev. D, 59, 044030, 1999.
R. Beig. TT-tensors and conformally flat structures on 3-manifolds. In P. Chruściel, ed., Mathematics of Gravitation, Part 1, vol. 41 (Banach Center Publications, Polish Academy of Sciences, Institute of Mathematics, Warszawa, 1997). Gr-qc/9606055.
R. Beig and N. O. Murchadha. Trapped surfaces due to concentration of gravitational radiation. Phys. Rev. Lett., 66, 2421–2424, 1991.
R. Beig and N. O. Murchadha. The momentum constraints of general relativity and spatial conformal isometries. Commun. Math. Phys., 176, 723–738, 1996.
R. Beig and N. O. Murchadha. Late time behavior of the maximal slicing of the Schwarzschild black hole. Phys. Rev. D, 57, 4728–4737, 1998.
R. Beig and W. Simon. Proof of a multipole conjecture due to Geroch. Commun. Math. Phys., 78, 75–82, 1980.
R. Beig and W. Simon. On the multipole expansion for stationary space-times. Proc. R. Lond. A, 376, 333–341, 1981.
J. M. Bowen and J. W. York, Jr. Time-asymmetric initial data for black holes and black-hole collisions. Phys. Rev. D, 21, 2047–2055, 1980.
S. Brandt and E. Seidel. The evolution of distorted rotating black holes III: Initial data. Phys. Rev. D, 54, 1403–1416, 1996.
D. Brill and R. W. Lindquist. Interaction energy in geometrostatics. Phys.Rev., 131, 471–476, 1963.
Y. Choquet-Bruhat, J. Isenberg, and J. W. York, Jr. Einstein constraint on asymptotically euclidean manifolds. Phys. Rev. D, 61, 084034, 1999. Gr-qc/9906095.
Y. Choquet-Bruhat and J. W. York, Jr. The Cauchy problem. In A. Held, ed., General Relativity and Gravitation, vol. 1, 99–172 (Plenum, New York, 1980).
S. Dain. Asymptotically flat initial data with prescribed regularity II, 2001. In preparation.
S. Dain. Initial data for a head on collision of two kerr-like black holes with close limit. Phys. Rev. D, 64, 124002, 2001. Gr-qc/0103030.
S. Dain. Initial data for stationary space-time near space-like infinity. Class. Quantum Grav., 18, 4329–4338, 2001. Gr-qc/0107018.
S. Dain and H. Friedrich. Asymptotically flat initial data with prescribed regularity. Comm. Math. Phys., 222, 569–609, 2001. Gr-qc/0102047.
S. Dain and G. Nagy. Initial data for fluid bodies in general relativity. Phys. Rev. D, 65, 084020, 2002. Gr-qc/0201091.
H. Friedrich. Cauchy problems for the conformal vacuum field equations in general relativity. Commun. Math. Phys., 91, 445–472, 1983.
H. Friedrich. On static and radiative space-time. Commun. Math. Phys., 119, 51–73, 1988.
H. Friedrich. Gravitational fields near space-like and null infinity. J. Geom. Phys., 24, 83–163, 1998.
P. R. Garabedian. Partial Differential Equations (John Wiley, New York, 1964).
R. Geroch. Multipole moments. II. curved space. J. Math. Phys., 11, 2580–2588, 1970.
D. Gilbarg and N. S. Trudinger. Elliptic Partial Differential Equations of Second Order (Springer-Verlag, Berlin, 1983).
R. J. Gleiser, G. Khanna, and J. Pullin. Evolving the Bowen-York initial data for boosted black holes. gr-qc/9905067, 1999.
S. W. Hawking. The event horizon. In C. DeWitt and B. S. DeWitt, eds., Black Holes, 1–56 (Gordon and Breach Science Publishers, New York, 1973).
P. Kundu. On the analyticity of stationary gravitational fields at spatial infinity. J. Math. Phys., 22, 2006–2011, 1981.
J. M. Lee and T. H. Parker. The Yamabe problem. Bull. Amer. Math. Soc., 17, 37–91, 1987.
R. C. McOwen. Partial Differential Equation (Prentice Hall, New Jersey, 1996).
C. W. Misner. Wormhole initial conditions. Phys.Rev., 118, 1110–1111, 1960.
C. W. Misner. The method of images in geometrostatics. Ann. Phys., 24, 102–117, 1963.
E. T. Newman and R. Penrose. Note on the Bondi-Metzner-Sachs group. J. Math. Phys., 7, 863–870, 1966.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Dain, S. (2002). Asymptotically Flat and Regular Cauchy Data. In: Frauendiener, J., Friedrich, H. (eds) The Conformal Structure of Space-Time. Lecture Notes in Physics, vol 604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45818-2_8
Download citation
DOI: https://doi.org/10.1007/3-540-45818-2_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44280-6
Online ISBN: 978-3-540-45818-0
eBook Packages: Springer Book Archive