2007/04/30 by Nirupam Roy, Arnab K. Ray · 1 citation
Mathematics · Physics and Astronomy · #Accretion (finance) #Black Holes and Theoretical Physics #Boundary value problem #Fractal #Fractal dimension #Fractional Differential Equations Solutions #Inflow #Perturbation (astronomy) #Quantum Electrodynamics and Casimir Effect #Transonic #astro-ph
paper · pdf · doi:10.1111/j.1365-2966.2007.12108.x
published as 2007, MNRAS, 380, 733 · 9 pages, 4 figures. Accepted for publication in MNRAS. The definitive version is available at http://www.blackwell-synergy.com
arxiv created 2007/07/18 · openalex publication_date 2007/08/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Spherically symmetric transonic accretion of a fractal medium has been studied in both the stationary and the dynamic regimes. The stationary transonic solution is greatly sensitive to infinitesimal deviations in the outer boundary condition, but the flow becomes transonic and stable when its evolution is followed through time. The evolution towards transonicity is more pronounced for a fractal medium than it is for a continuum, and in the former case the static sonic condition is met on relatively larger length scales. The dynamic approach also shows that there is a remarkable closeness between an equation of motion for a perturbation in the flow, and the metric of an analogue acoustic black hole. The stationary inflow solutions of a fractal medium are as much stable under the influence of linearized perturbations as they are for the fluid continuum.