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We give a new proof for the existence of spherically symmetric steady states to the Vlasov-Poisson system, following a strategy that has been used successfully to approximate axially symmetric solutions numerically, both to the Vlasov-Poisson system
Externí odkaz:
http://arxiv.org/abs/2412.01544
Autor:
Andréasson, Håkan, Rein, Gerhard
In 1939, Oppenheimer and Snyder showed that the continued gravitational collapse of a self-gravitating matter distribution can result in the formation of a black hole, cf.~ \cite{OS}. In this paper, which has greatly influenced the evolution of ideas
Externí odkaz:
http://arxiv.org/abs/2410.06701
Autor:
Andréasson, Håkan, Kunze, Markus
In 2001 Wolansky \cite{Wol} introduced a particle number-Casimir functional for the Einstein-Vlasov system. Two open questions are associated with this functional. First, a meaningful variational problem should be formulated and the existence of a mi
Externí odkaz:
http://arxiv.org/abs/2402.10657
We rigorously derive the quadrupole formula within the context of the Einstein-Vlasov system. The main contribution of this work is an estimate of the remainder terms, derived from well-defined assumptions, with explicitly stated error terms that dep
Externí odkaz:
http://arxiv.org/abs/2309.00431
Autor:
Andréasson, Håkan, Kunze, Markus
Publikováno v:
SIAM J. Math. Anal. 55, 4843-4879 (2023)
Existence of spherically symmetric solutions to the Einstein-Vlasov system is well-known. However, it is an open problem whether or not static solutions arise as minimizers of a variational problem. Apart from being of interest in its own right, it i
Externí odkaz:
http://arxiv.org/abs/2202.01835
Autor:
Andréasson, Håkan
Publikováno v:
Ann. H. Poincar\'e 22, 4271-4297 (2021)
We show that there exist steady states of the massless Einstein-Vlasov system which surround a Schwarzschild black hole. The steady states are (thick) shells with finite mass and compact support. Furthermore we prove that an arbitrary number of shell
Externí odkaz:
http://arxiv.org/abs/2102.08170
We numerically investigate the dynamics near black hole formation of solutions to the Einstein--Vlasov system in axisymmetry. Our results are obtained using a particle-in-cell and finite difference code based on the $(2+1)+1$ formulation of the Einst
Externí odkaz:
http://arxiv.org/abs/2010.15771
Akademický článek
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Autor:
Andréasson, Håkan, Kunze, Markus
Publikováno v:
Arch. Ration. Mech. Anal. 235, 783-791 (2020)
In this note we address the attempted proof of the existence of static solutions to the Einstein-Vlasov system as given in \cite{Wol}. We focus on a specific and central part of the proof which concerns a variational problem with an obstacle. We show
Externí odkaz:
http://arxiv.org/abs/1805.10683
Publikováno v:
Phys. Rev. D 99, 024012 (2019)
We numerically investigate limits of a two-parameter family of stationary solutions to the Einstein-Vlasov system. The solutions are toroidal and have non-vanishing angular momentum. As one tunes to more relativistic solutions (measured for example b
Externí odkaz:
http://arxiv.org/abs/1803.11224