N-body gravity and the Schrödinger equation

2006/11/30 by P. S. Farrugia, P S Farrugia, Robert B. Mann +3 · 18 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Gravitation #Mathematical physics #Physics #Pulsars and Gravitational Waves Research #gr-qc

paper · pdf · doi:10.1088/0264-9381/24/18/006

published in Classical and Quantum Gravity 24(18), 4647-4659 (IOP Publishing) · 15 pages, Latex, references added, typos corrected, final version that appears in CQG

openalex publication_date 2007/08/30 · arxiv created 2007/09/06 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We consider the problem of the motion of N bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum–mechanical problem of an N -body generalization of the problem of the H + 2 molecular ion in one dimension. The canonical gravitational N -body formalism can be extended to include electromagnetic charges. We derive a general algorithm for solving this problem, and show how it reduces to known results for the 2-body and 3-body systems.

Citations

• Conserved masses in GHS Einstein and string black holes and consistent thermodynamics
• Energy for N -body motion in two-dimensional gravity
• The D to 2 limit of general relativity
• Canonical reduction of two-dimensional gravity for particle dynamics
• Exact solution for relativistic two-body motion in dilaton gravity

Cited by

• Canonical reduction for dilatonic gravity in 3+1 dimensions