On spherically symmetric solutions of the Einstein-Euler equations

DOI10.1215/21562261-3478880zbMath1351.35220arXiv1410.1234OpenAlexW3103892372MaRDI QIDQ294143

Tetu Makino

Publication date: 9 June 2016

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.1234

zbMATH Keywords

Einstein equationsspherically symmetric solutionsNash-Moser theoremTolman-Oppenheimer-Volkoff equationsvacuum boundary

Mathematics Subject Classification ID

Gas dynamics (general theory) (76N15) Second-order nonlinear hyperbolic equations (35L70) Wave equation (35L05) Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Hydrodynamic and hydromagnetic problems in astronomy and astrophysics (85A30) Einstein equations (35Q76) Initial value problems for second-order hyperbolic systems (35L52) Initial-boundary value problems for higher-order hyperbolic systems (35L57)

Related Items (10)

Local stability to the Einstein-Euler system in Schwarzschild space-time ⋮ The relativistic Euler equations with a physical vacuum boundary: Hadamard local well-posedness, rough solutions, and continuation criterion ⋮ On slowly rotating axisymmetric solutions of the Einstein-Euler equations ⋮ An application of the Nash-Moser theorem to the vacuum boundary problem of gaseous stars ⋮ On the asymptotic behavior of static perfect fluids ⋮ Turning point principle for relativistic stars ⋮ Dynamics of gravitational collapse in the axisymmetric Einstein–Vlasov system ⋮ On the axisymmetric metric generated by a rotating perfect fluid with the vacuum boundary ⋮ Stability and instability of self-gravitating relativistic matter distributions ⋮ Monotone-short solutions of the Tolman-Oppenheimer-Volkoff-de Sitter equation

Cites Work

• Local existence of solutions of self gravitating relativistic perfect fluids
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• On spherically symmetric motions of a gaseous star governed by the Euler-Poisson equations
• Existence and properties of spherically symmetric static fluid bodies with a given equation of state
• On Spherically Symmetric Motions of the Atmosphere Surrounding a Planet Governed by the Compressible Euler Equations
• The inverse function theorem of Nash and Moser
• On Massive Neutron Cores
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