Tensor expression for solving Einstein's equations by the method of sequential approximation
type: Item
instance of: scholarly article
title: Tensor expression for solving Einstein's equations by the method of sequential approximation
zbMATH Open document ID: 0879.53057
DOI: 10.1023/A:1018843318622
author: I. P. Denisova
author: Binita V. Mehta
published in: General Relativity and Gravitation
publication date: 1997-08-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 83C05
zbMATH DE Number: 1040649
zbMATH Keywords: sequential approximation
zbMATH Keywords: perturbed metric tensor
zbMATH Keywords: determinant
Wikidata QID: Q114394863
reviewed by: Chandra Shekhar Sharma
MaRDI profile type: Publication
cites work: Q4748786
full work available at URL: a:1018843318622
OpenAlex ID: W109449756
description: scientific article; zbMATH DE number 1040649