2018/12/11 by Georgios Moschidis, Moschidis, Georgios
Mathematics · Physics and Astronomy · #83C57 (Primary) 35L53 (Secondary) #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1812.04268
openalex publication_date 2018/12/11 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28
In recent years, the AdS instability conjecture, put forward by Dafermos-Holzegel in 2006, has attracted a substantial amount of numerical and heuristic studies. Following the pioneering work of Bizon-Rostworowski, research efforts have been mainly focused on the study of the spherically symmetric Einstein-scalar field system. The first rigorous proof of the instability of AdS in the simplest spherically symmetric setting, namely for the Einstein-null dust system, was obtained in [G. Moschidis, A proof of the instability of AdS for the Einstein-null dust system with an inner mirror, 2017, arXiv:1704.08681]. In that work, the evolution was restricted to the exterior of an inner mirror placed at r=r0>0, in order to circumvent the trivial break down of the Einstein-null dust system occurring at r=0; in that setting, additional considerations necessitated r0 to shrink to 0 with the size of the initial perturbation. In this paper, we establish the instability of AdS for the Einstein-massless Vlasov system in spherical symmetry. This will be the first proof of the AdS instability conjecture for an Einstein--matter system which is well-posed for regular initial data in the standard sense, without the addition of an inner mirror. New difficulties associated with the Einstein-massless Vlasov system (such as the need for control on the paths of non-radial geodesics in a large curvature regime) force us to develop a strategy of proof which is fundamentally different from the one employed in the case of the Einstein--null dust system, albeit still based on the interaction of beams of matter in physical space.