Newton–Hooke spacetimes, Hpp-waves and the cosmological constant

2003/08/28 by G. W. Gibbons, G W Gibbons, C. E. Patricot +1 · 7 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #astro-ph #gr-qc #hep-th

paper · pdf · doi:10.1088/0264-9381/20/23/016

published as Class.Quant.Grav.20:5225,2003 · 21 pages

arxiv created 2003/08/28 · openalex publication_date 2003/10/24 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

We show explicitly how the Newton–Hooke groups N ± 10 act as symmetries of the equations of motion of non-relativistic cosmological models with a cosmological constant. We give the action on the associated non-relativistic spacetimes M ± 4 and show how these may be obtained from a null reduction of five-dimensional homogeneous pp-wave Lorentzian spacetimes M ± 5 . This allows us to realize the Newton–Hooke groups and their Bargmann-type central extensions as subgroups of the isometry groups of M ± 5 . The extended Schrödinger-type conformal group is identified and its action on the equations of motion given. The non-relativistic conformal symmetries also have applications to time-dependent harmonic oscillators. Finally we comment on a possible application to Gao's generalization of the matrix model.

Citations

• Bargmann structures and Newton-Cartan theory
• Possible Kinematics

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