On the Nonexistence of a Class of Static Einstein Spaces Asymptotic at Infinity to a Space of Constant Curvature
- 1 November 1960
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 1 (6) , 537-541
- https://doi.org/10.1063/1.1703690
Abstract
It is known that there exist no nontrivial static regular solutions of the Einstein vacuum equations Rkl=0 which are asymptotically Galilean at infinity. One may ask correspondingly whether there exist static solutions of the equations Rkl=λgkl(λ<0) which are regular at all finite points and asymptotic (in a sense to be defined) to a space of constant curvature at infinity. The answer to this question is here shown to be in the negative. The proof rests upon the possibility of writing a certain quadratic invariant density of the Riemann tensor in the form of an ordinary divergence.Keywords
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