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STATIC SOLUTIONS TO...
STATIC SOLUTIONS TO THE SPHERICALLY SYMMETRIC EINSTEIN-VLASOV SYSTEM: A PARTICLE NUMBER-CASIMIR APPROACH
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- Andreasson, Håkan, 1966 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Kunze, Markus (author)
- Universität zu Köln,University of Cologne
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(creator_code:org_t)
- 2023
- 2023
- English.
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In: SIAM Journal on Mathematical Analysis. - 1095-7154 .- 0036-1410. ; 55:5, s. 4843-4879
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Abstract
Subject headings
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- The existence of nontrivial static 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 is the connection to nonlinear stability that gives this topic its importance. This problem was considered in [G. Wolansky, Arch. Ration. Mech. Anal., 156 (2001), pp. 205-230], but as has been pointed out in [H. Andr\'easson and M. Kunze, Arch. Ration. Mech. Anal., 235 (2020), pp. 783-791], that paper contained serious flaws. In this work we construct static solutions by solving the Euler- Lagrange equation for the energy density ρ as a fixed point problem. The Euler-Lagrange equation originates from the particle number-Casimir functional introduced in Wolansky (2001). We then define a density function f on phase space which induces the energy density \rho and we show that it constitutes a static solution of the Einstein-Vlasov system. Hence we settle rigorously parts of what Wolansky (2001) attempted to prove.
Subject headings
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- variational problem
- Einstein-Vlasov system
- static solutions
- Einstein-Vlasov system
- static solutions
- variational problem
Publication and Content Type
- art (subject category)
- ref (subject category)
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