There exist no 4-dimensional geodesically equivalent metrics with the same stress energy tensor

JOURNAL OF GEOMETRY AND PHYSICS

卷:78

Article

Kiosak, Volodymyr¹  Matveev, Vladimir S.¹ 

[1] FSU Jena, Inst Math, D-07737 Jena, Germany

关键词: Geodesically equivalent metrics;    Einstein field equation;    Warped product metrics;   

DOI  :  10.1016/j.geomphys.2014.01.002

来源: Elsevier

【 摘 要 】

We show that if two 4-dimensional metrics of arbitrary signature on one manifold are geodesically equivalent (i.e., have the same geodesics considered as unparameterized curves) and are solutions of the Einstein field equation with the same stress energy tensor, then they are affinely equivalent or flat. If we additionally assume that the metrics are complete or that the manifold is closed, the result remains valid in all dimensions >= 3. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free