Skip to main content
SpringerLink
Log in

On the relation between ADM and Bondi energymomenta III-perturbed radiative spatial infinity

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

In a vacuum spacetime equipped with the Bondi’s radiating metric which is asymptotically flat at spatial infinity including gravitational radiation (Condition D), we establish the relation between the ADM total energy-momentum and the Bondi energy-momentum for perturbed radiative spatial infinity. The perturbation is given by defining the “real” time as the sum of the retarded time, the Euclidean distance and certain function f.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ashtekar A, Magnon-Ashtekar A. Energy-momentum in general relativity. Phys Rev Lett, 43: 181–184 (1979)

    Article  MathSciNet  Google Scholar 

  2. Hayward S. Spatial and null infinity via advanced and retarded conformal factors. Phys Rev D, 68: 104015 (2003)

    Article  MathSciNet  Google Scholar 

  3. Valiente Kroon J. Early radiative properties of the developments of time-symmetric conformally flat initial data. Class Quantum Grav, 20: L53–L59 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Valiente Kroon J. Does asymptotic simplicity allow for radiation near spatial infinity. Commun Math Phys, 251: 211–234 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  5. Christodoulou D, Klainerman S. The Global Nonlinear Stablity of Minkowski Space. Princeton Math. Series 41, Princeton: Princeton University. Press, 1993

    Google Scholar 

  6. Zhang X. On the relation between ADM and Bondi energy-momenta. Adv Theor Math Phys, 10: 261–282 (2006)

    MATH  MathSciNet  Google Scholar 

  7. Huang W L, Zhang X. On the relation between ADM and Bondi energy-momenta II-radiative spatial infinity, gr-qc/0511037

  8. Chruściel P, MacCallum M, Singleton D. Gravitational waves in general relativity XIV, Bondi expansions and the “polyhomogeneity” of Scri. Phil Trans Roy Soc A, 350: 113–141 (1995)

    Article  MATH  Google Scholar 

  9. Bondi H, van der Burg M, Metzner A. Gravitational waves in general relativity VII, Waves from axisymmetric isolated systems. Proc Roy Soc London A, 269: 21–52 (1962)

    Article  MATH  Google Scholar 

  10. Sachs R. Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time. Proc Roy Soc London A, 270: 103–126 (1962)

    MATH  MathSciNet  Google Scholar 

  11. van der Burg M. Gravitational waves in general relativity IX, Conserved quantities. Proc Roy Soc London A, 294: 112–122 (1966)

    Google Scholar 

  12. Arnowitt S, Deser S, Misner C. Coordinate invariance and energy expressions in general relativity. Phys Rev, 122: 997–1006 (1961)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department Mathematik, Schwerpunkt GD, Universität Hamburg, Bundesstr. 55, D-20146, Hamburg, Germany

    Wen-ling Huang

  2. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Xiao Zhang

Authors
  1. Wen-ling Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiao Zhang.

Additional information

This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 10231050, 10421001), the National Key Basic Research Project of China (Grant No. 2006CB805905) and the Innovation Project of Chinese Academy of Sciences

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, Wl., Zhang, X. On the relation between ADM and Bondi energymomenta III-perturbed radiative spatial infinity. SCI CHINA SER A 50, 1316–1324 (2007). https://doi.org/10.1007/s11425-007-0074-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-007-0074-8

Keywords

MSC(2000)

Search

Navigation