General Relativity and Gravitation

, Volume 7, Issue 10, pp 809–815 | Cite as

On the existence of a general rotating solution of Einstein's equations

  • Jamal N. Islam
Research Articles


In an earlier paper we considered a power-series expansion of the metric for a rotating field in terms of a parameter and constructed a solution of Einstein's equations to the first few orders in terms of two harmonic functions. We encountered a pair of Poisson-type equations which were apparently insoluble explicitly. The form of the metric considered was the Weyl-Lewis-Papapetrou form. In this paper we consider a power-series expansion of the most general form of a rotating metric and show that one encounters the same two Poisson equations as before. If these equations are insoluble explicitly, as seems likely, then a general solution depending on two harmonic functions cannot exist in closed form.


General Solution Harmonic Function Closed Form Differential Geometry Early Paper 
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Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Jamal N. Islam
    • 1
  1. 1.Department of Applied Mathematics and AstronomyUniversity CollegeCardiffUK

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