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.

References in corpus (2)

• Strong cosmic censorship for T^2-symmetric cosmological spacetimes with collisionless matter
• Variational principle for the Einstein-Vlasov equations

Cited by in corpus (5)

• Stability and instability results for equilibria of a (relativistic) self-gravitating collisionless gas -- A review
• Axisymmetric, stationary collisionless gas configurations surrounding black holes
• Accretion of a Vlasov gas by a Kerr black hole
• Spherical accretion of a collisionless kinetic gas into a generic static black hole
• A Birman-Schwinger Principle in General Relativity: Linearly Stable Shells of Collisionless Matter Surrounding a Black Hole