2006/07/11 by Jessica Rosen, Jae-Hun Jung, Gaurav Khanna · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary value problem #Classical mechanics #Computer science #Constraint (computer-aided design) #Cosmology #Cosmology and Gravitation Theories #Geometry #Loop quantum cosmology #Loop quantum gravity #Mathematical physics #Mathematics #Neumann boundary condition #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum gravity #Quantum mechanics #Stability (learning theory) #Theoretical physics #Von Neumann stability analysis #gr-qc
paper · pdf · doi:10.1088/0264-9381/23/23/028
published as Class.Quant.Grav. 23 (2006) 7075-7084 · 6 pages, 8 figures
arxiv created 2006/07/11 · openalex publication_date 2006/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we perform the von Neumann analysis of the difference equations that arise as a result of loop quantum gravity being applied to models of cosmology and black holes. In particular, we study the numerical stability of Bianchi I locally rotationally symmetric (symmetric and non-symmetric constraint) and Schwarzschild interior (symmetric constraint) models, and find that there exist domains over which there are instabilities, generically. We also present explicit evolutions of wave-packets in these models and clearly demonstrate the presence of these instabilities.