2008/09/28 by Jennie D’Ambroise, Jennie D'Ambroise, D'Ambroise, Jennie
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc
paper · pdf · doi:10.48550/arxiv.0809.4817
arxiv created 2008/09/28 · openalex publication_date 2008/09/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using a conformal version of the Bianchi I metric and a perfect fluid energy-momentum tensor, we show that the resulting Einstein field equations are equivalent to a generalized Ermakov-Milne-Pinney equation. Using a transformation analogous to the known correspondence between the classical EMP and a linear Schrödinger equation, we then construct the linear Schrödinger formulation for this cosmological model. Also, a note is included to show the extra term that arises when the energy-momentum tensor is taken to include a second term in addition to the scalar field.