2015/03/17 by Patryk Mach · 15 citations
Physics and Astronomy · #Accretion (finance) #Astrophysical Phenomena and Observations #Astrophysics #Bifurcation #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #General relativity #Homoclinic orbit #Mathematical physics #Mechanics #Nonlinear system #Physics #Polytropic process #Quantum mechanics #Schwarzschild metric #Schwarzschild radius #Spacetime #Transonic #gr-qc
paper · pdf · doi:10.1103/physrevd.91.084016
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 91(8) (American Physical Society) · 6 pages, 2 figures, to appear in Physical Review D
arxiv created 2015/03/17 · openalex publication_date 2015/04/07 · arxiv updated 2015/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The aim of this paper is to clarify the distinction between homoclinic and standard (global) Bondi-type accretion solutions in the Schwarzschild--anti--de Sitter space-time. The homoclinic solutions have recently been discovered numerically for polytropic equations of state. Here I show that they exist also for certain isothermal (linear) equations of state, and an analytic solution of this type is obtained. It is argued that the existence of such solutions is generic, although for sufficiently relativistic matter models (photon gas, ultrahard equation of state) there exist global solutions that can be continued to infinity, similarly to standard Michel's solutions in the Schwarzschild space-time. In contrast to that global solutions should not exist for matter models with a nonvanishing rest-mass component, and this is demonstrated for polytropes. For homoclinic isothermal solutions I derive an upper bound on the mass of the black hole for which stationary transonic accretion is allowed.