Stability and Instability of Self-Gravitating Relativistic Matter Distributions

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