Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime

Abstract

This paper proves the existence of a bounded energy and integrated energy decay for solutions of the massless Vlasov equation in the exterior of a very slowly rotating Kerr spacetime. This combines methods previously developed to prove similar results for the wave equation on the exterior of a very slowly rotating Kerr spacetime with recent work applying the vector-field method to the relativistic Vlasov equation.

18 pages

References in corpus (4)

• Accretion of a relativistic, collisionless kinetic gas into a Schwarzschild black hole
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• Ultimately Schwarzschildean Spacetimes and the Black Hole Stability Problem
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Cited by in corpus (25)

• An introduction to the relativistic kinetic theory on curved spacetimes
• The Stability of the Minkowski space for the Einstein-Vlasov system
• Lux in obscuro: Photon Orbits of Extremal Black Holes Revisited
• Boundedness of massless scalar waves on Kerr interior backgrounds
• Sharp asymptotic behavior of solutions of the $3d$ Vlasov-Maxwell system with small data
• Accretion of the relativistic Vlasov gas in the equatorial plane of the Kerr black hole
• The Strauss conjecture on asymptotically flat space-times
• A vector field method for massless relativistic transport equations and applications
• Nonlinear radiation gauge for near Kerr spacetimes
• Strichartz estimates on Kerr black hole backgrounds
• Sharp asymptotics for the solutions of the three-dimensional massless Vlasov-Maxwell system with small data
• Price's Law on Nonstationary Spacetimes
• Decay estimates for the massless Vlasov equation on Schwarzschild spacetimes
• On the global stability of the wave-map equation in Kerr spaces with small angular momentum
• Timelike and null geodesics in the Schwarzschild space-time: Analytical solutions
• Spherical accretion of a collisionless kinetic gas into a generic static black hole
• Accretion of the degenerate Fermi gas onto a Reissner-Nordström black hole
• Linear stability of Schwarzschild spacetime subject to axial perturbations
• Stability study of a model for the Klein-Gordon equation in Kerr spacetime
• Resolvent estimates with mild trapping
• Decay and non-decay for the massless Vlasov equation on subextremal and extremal Reissner-Nordström black holes
• Stability study of a model for the Klein-Gordon equation in Kerr space-time II
• Superradiance or total reflection?
• Relatively non-degenerate integrated decay estimates for massless Vlasov fields on Schwarzschild spacetimes
• Existence of steady states of the massless Einstein-Vlasov system surrounding a Schwarzschild black hole