Skip to main content Accessibility help
×
×
Home

On the static field in general relativity

  • Jamal N. Islam (a1)
Abstract

The possibility is explored that the general static solution of Einstein's vacuum field equations is given in terms of a single harmonic function, i.e. solution of the flat space Laplace equation. It is shown that coordinate conditions can be chosen such that one of Einstein's equations reduces to Laplace's equation. To examine the extent to which the metric is determined by the resulting harmonic function ø, a power series expansion is considered in which in the first non-trivial order one gets a system of eight equations for six unknowns. This is reduced to a system of three equations for three unknowns. This is some indication that the coordinate conditions are consistent and shows the sense in which, to this order, the metric is determined by ø. This system of three equations is then solved explicitly for a particular choice of ø, thereby giving an approximate non-axisymmetric solution of Einstein's vacuum equations. This solution is asymptotically flat and could represent the approximate gravitational field of a non-axisymmetric bounded rigid body. The form of a class of time-dependent metric related to the general static metric is discussed.

Copyright
References
Hide All
(1)Brurat, Y. In Gravitation, an introduction to current research, ed. Witten, L. (Wiley, 1962).
(2)Einstein, A. and Rosen, N. J.Franklin Inst. 223 (1937), 43.
(3)Einstein, A., Infeld, L. and Hoffman, B.Ann. Math. 39 (1938), 65.
(4)Weyl, H.Ann. Physik. 54 (1917), 117.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed