General relativistic shock waves that extend the Oppenheimer-Snyder model

Archive for Rational Mechanics and Analysis

Volumn 138, Issue 3, 1997, Pages 239-277

  Smoller, Joel ^a   Temple, Blake ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; FLUID DYNAMICS; INTERFACES (MATERIALS); MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; RELATIVITY; ASTROPHYSICS; DIFFERENTIAL EQUATIONS; SPEED; THEOREM PROVING;

FRIEDMANN-ROBERTSON-WALKER METRIC; OPPENHEIMER-SNYDER RESULT; EINSTEIN EQUATION; OPPENHEIMER-SNYDER MODEL; ORDINARY DIFFERENTIAL EQUATION;

SHOCK WAVES;

EID: 0031282921     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050041     Document Type: Article

References (11)

1. W. ISRAEL, Singular hypersurfaces and thin shells in general relativity, II Nuovo Cimento, 44 B (1966), 1-14.
2. P. D. LAX, Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math., 10 (1957), 537-566.
3. J. R. OPPENHEIMER & J. R. SNYDER, On continued gravitational contraction, Phys. Rev., 56 (1939), 455-459.
4. J. SMOLLER, Shock-Waves and Reaction-Diffusion Equations, Second edn., Springer-Verlag, 1994.
5. J. SMOLLER, B. TEMPLE & Z. P. XIN, Instability of rarefaction shocks for systems of conservation laws, Arch. Rational Mech. Anal., 112, (1990), 63-81.
6. J. SMOLLER & B. TEMPLE, Global solutions of the relativistic Euler equations, Comm. Math. Phys., 157 (1993), 67-99.
7. J. SMOLLER & B. TEMPLE, Shock-wave solutions of the Einstein equations: The Oppenheimer-Snyder model of gravitational collapse extended to the case of non-zero pressure. Arch. Rational Mech. Anal., 128 (1994), 249-297.
8. J. SMOLLER & B. TEMPLE, Astrophysical shock-wave solutions of the Einstein equations, Phys. Rev. D, 51 (1995), 2733-2743.
9. R. TOLMAN, Static solutions of Einstein 's field equations for spheres of fluid, Phys. Rev., 55(1939), 364-374.
10. R. TOLMAN, Relativity, Thermodynamics and Cosmology, Oxford University Press, 1934.
11. S. WEINBERG, Gravitation and Cosmology. Principles and Applications of the General Theory of Relativity, Wiley, New York, 1972.