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- W3163021167 abstract "We consider steady state solutions of the massive, asymptotically flat, spherically symmetric Einstein-Vlasov system, i.e., relativistic models of galaxies or globular clusters, and steady state solutions of the Einstein-Euler system, i.e., relativistic models of stars. Such steady states are embedded into one-parameter families parameterized by their central redshift $kappa>0$. We prove their linear instability when $kappa$ is sufficiently large, i.e., when they are strongly relativistic, and that the instability is driven by a growing mode. Our work confirms the scenario of dynamic instability proposed in the 1960s by Zel'dovich & Podurets (for the Einstein-Vlasov system) and by Harrison, Thorne, Wakano, & Wheeler (for the Einstein-Euler system). Our results are in sharp contrast to the corresponding non-relativistic, Newtonian setting. We carry out a careful analysis of the linearized dynamics around the above steady states and prove an exponential trichotomy result and the corresponding index theorems for the stable/unstable invariant spaces. Finally, in the case of the Einstein-Euler system we prove a rigorous version of the turning point principle which relates the stability of steady states along the one-parameter family to the winding points of the so-called mass-radius curve." @default.
- W3163021167 created "2021-05-24" @default.
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- W3163021167 date "2021-05-10" @default.
- W3163021167 modified "2023-10-16" @default.
- W3163021167 title "Stability and Instability of Self-Gravitating Relativistic Matter Distributions" @default.
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- W3163021167 doi "https://doi.org/10.1007/s00205-021-01647-2" @default.
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