There are no conformal Einstein rescalings of complete pseudo-Riemannian Einstein metrics (Q841294)

The authors study properties of pseudo-Riemannian Einstein metrics. It is shown that if \(g\) is a light-line-complete pseudo-Riemannian Einstein metric of indefinite signature on a connected \(n\)-dimensional manifold \(M\) and if \(\psi^{-2}g\) is also Einstein, then \(\psi\) is constant. Also, the authors show that if \(g\) is a pseudo-Riemannian Einstein metric of indefinite signature on a connected closed \(n\)-dimensional manifold \(M\) and if \(\psi^{-2}g\) is also Einstein, then \(\psi\) is constant.