Abstract
The aim of this paper is to investigate the static perfect fluid spacetime \(M^{4}\times _{f}\mathbb {R}\) such that \((M^4, g)\) is a half conformally flat Riemannian manifold. We prove that \((M^4, g)\) is, in fact, locally isometric to a warped product manifold \(I\times _{\phi }N^{3}\) where \(I\subset \mathbb {R}\) and \(N^{3}\) is a space form. Consequently, we make an analysis of the Fischer-Marsden conjecture for a 4-dimensional Riemannian manifold.
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Leandro, B., Solórzano, N. Static perfect fluid spacetime with half conformally flat spatial factor. manuscripta math. 160, 51–63 (2019). https://doi.org/10.1007/s00229-018-1042-z
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DOI: https://doi.org/10.1007/s00229-018-1042-z