2015/12/27 by Philippe G. LeFloch, LeFloch, Philippe G., Shuyang Xiang +1
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.AP
paper · pdf · doi:10.48550/arxiv.1512.08253
49 pages
arxiv created 2015/12/27 · openalex publication_date 2015/12/27 · arxiv updated 2015/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the global dynamics of isothermal fluids evolving in the domain of outer communication of a Schwarzschild black hole. We first formulate the initial value problem within a class of weak solutions with bounded variation (BV), possibly containing shock waves. We then introduce a version of the random choice method and establish a global-in-time existence theory for the initial value problem within the proposed class of weakly regular fluid flows. The initial data may have arbitrary large bounded variation and can possibly blow up near the horizon of the black hole. Furthermore, we study the class of possibly discontinuous, equilibrium solutions and design a version of the random choice method in which these fluid equilibria are exactly preserved. This leads us to a nonlinear stability property for fluid equilibria under small perturbations with bounded variation. Furthermore, we can also encompass several limiting regimes (stiff matter, non-relativistic flows, extremal black hole) by letting the physical parameters (mass of the black hole, light speed, sound speed) reach extremal values.