Newtonian approximation in (1 + 1) dimensions. (1st December 2022)

• Record Type: Journal Article
• Authors: Casadio, Roberto; Micu, Octavian; Mureika, Jonas
• Is Part Of: Physica scripta. Volume 97:Number 12(2022)
• Publication Date: 2022-12-01
• Subjects: newtonian limit -- dimensional reduction -- quantum gravity; Physics -- Periodicals; 530.05
• DOI: 10.1088/1402-4896/ac9e80
• Languages: English
• ISSNs: 0031-8949

Abstract

Abstract: We study the possible existence of a Newtonian regime of gravity in 1 + 1 dimensions, considering metrics in both the Kerr-Schild and conformal forms In the former case, the metric gives the exact solution of the Poisson equation in flat space, but the weak-field limit of the solutions and the non-relativistic regime of geodesic motion are not trivial. We show that using harmonic coordinates, the metric is conformally flat and a weak-field expansion is straightforward. An analysis of the non-relativistic regime of geodesic motion remains non-trivial and the weak-field potential only satisfies the flat space Poisson equation approximately.