Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-16T17:21:56.258Z Has data issue: false hasContentIssue false
  • English
  • Français

Quadratic Langrangians and static gravitational fields

Published online by Cambridge University Press:  24 October 2008

H. A. Buchdahl
H. A. Buchdahl
Affiliation:
Australian National University, Canberra
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that the solutions of the field equations generated by the most general effective quadratic Lagrangian aR2 + bRklRkl which are static, singularity-free, of class C4 and asymptotically flat (of rank A3) are (i) conformally flat when 3a + b = 0, (ii) flat when 3a + b ≠ 0 (b ≠ 0), and (iii) have zero scalar curvature when b = 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 145 - 148
Copyright
Copyright © Cambridge Philosophical Society 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Buchdahl, H. A.The Hamiltonian derivatives of a class of fundamental invariants. Quart. J. Math. (Oxford) 19 (1948), 150.Google Scholar
(2)Buchdahl, H. A.On the non-existence of a class of static Einstein spaces asymptotic at infinity to a space of constant curvature. J. Math. and Phys. 1 (1960), 537.Google Scholar
(3)Courant, R. and Hilbert, D.Methods of Mathematical Physics, vol. II (Interscience, 1966), p. 326.Google Scholar
(4)Eddington, A. S.The mathematical theory of relativity (Cambridge University Press, 1923), §62.Google Scholar
(5)Fock, V.The theory of space, time and gravitation (Pergamon Press, 1959), p. 188.Google Scholar
(6)Petrow, A. S.Einstein-Räume (Akademie Verlag, 1964), §22.Google Scholar