Static spherically symmetric Einstein-Vlasov bifurcations of the Schwarzschild spacetime

Abstract

We construct a one-parameter family of static and spherically symmetric solutions to the Einstein-Vlasov system bifurcating from the Schwarzschild spacetime. The constructed solutions have the property that the spatial support of the matter is a finite, spherically symmetric shell located away from the black hole. Our proof is mostly based on the analysis of the set of trapped timelike geodesics and of the effective potential energy for static spacetimes close to Schwarzschild. This provides an alternative approach to the construction of static solutions to the Einstein-Vlasov system in a neighbourhood of black hole vacuum spacetimes.

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• Asymptotic Stability of Minkowski Space-Time with non-compactly supported massless Vlasov matter
• A Birman-Schwinger Principle in General Relativity: Linearly Stable Shells of Collisionless Matter Surrounding a Black Hole
• Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole