Tensor expression for solving Einstein's equations by the method of sequential approximation
This paper seems to solve the following problem: Given \[ g_{ik}=g_{ik}^{(0)}+\Psi_{ik} \] where both \(g_{ik}^{(0)}\) and \(\Psi_{ik}\) are known, find a much more complicated expression for \(g_{ik}\) using the so-called \(S\)-th power of \(\Psi_{ik}\) defined by \[ \Psi_{ik}^{(0)}=g_{ik}^{(0)}\quad \text{for}\quad S=0, \] \[ \Psi_{ik}^{(S)}=\Psi_{im}g^{(0)mn}\Psi_{nk}^{(S-1)}\quad \text{for}\quad S\geq 0 . \] Formulae for \(g_{ij}\) and \(\det g_{ij}\) using powers of \(\Psi_{ik}\) up to the fourth are obtained. These complicated formulae are supposed to provide important tools for general relativity.
scientific article; zbMATH DE number 1040649