2021/12/20 by Yan Guo, Guo, Yan, Mahir Hadžić +3 · 1 citation
Mathematics · Physics and Astronomy · #35Q35 #35Q76 #37N20 #83C75 #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2112.10826
openalex publication_date 2021/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 1990, based on numerical and formal asymptotic analysis, Ori and Piran predicted the existence of self-similar spacetimes, called relativistic Larson-Penston solutions, that can be suitably flattened to obtain examples of spacetimes that dynamically form naked singularities from smooth initial data, and solve the radially symmetric Einstein-Euler system. Despite its importance, a rigorous proof of the existence of such spacetimes has remained elusive, in part due to the complications associated with the analysis across the so-called sonic hypersurface. We provide a rigorous mathematical proof. Our strategy is based on a delicate study of nonlinear invariances associated with the underlying non-autonomous dynamical system to which the problem reduces after a self-similar reduction. Key technical ingredients are a monotonicity lemma tailored to the problem, an ad hoc shooting method developed to construct a solution connecting the sonic hypersurface to the so-called Friedmann solution, and a nonlinear argument to construct the maximal analytic extension of the solution. Finally, we reformulate the problem in double-null gauge to truncate the self-similar profile and thus obtain an asymptotically flat spacetime with an isolated naked singularity.