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Shock waves in classical dust collapse

Viqar Husain* and Hassan Mehmood†

  • *Contact author: vhusain@unb.ca
  • †Contact author: hassan.mehmood@unb.ca
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Phys. Rev. Research 7, 033215 – Published 3 September, 2025

DOI: https://doi.org/10.1103/b317-86qs

Abstract

During gravitational collapse of dust in spherical symmetry, matter particles may collide forming shell crossing singularities (SCSs) at which the Einstein equations become indeterminate. We show that in the case of marginally bound dust collapse, there is a unique evolution beyond SCSs such that a propagating shock wave forms, the metric remains continuous, and the stress-energy tensor dynamically becomes that of a thin shell. We give numerical simulations that exhibit this result.

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References (32)

  1. P. C. Vaidya, Nonstatic solutions of Einstein’s field equations for spheres of fluids radiating energy, Phys. Rev. 83, 10 (1951).
  2. V. Husain, Exact solutions for null fluid collapse, Phys. Rev. D 53, R1759 (1996).
  3. H. Bondi, Spherically symmetrical models in general relativity, Mon. Not. R. Astron. Soc. 107, 410 (1947).
  4. R. C. Tolman, Effect of imhomogeneity on cosmological models, Proc. Natl. Acad. Sci. USA 20, 169 (1934).
  5. P. Yodzis, H. Seifert, and H. M. Zum Hagen, On the occurrence of naked singularities in general relativity, Commun. Math. Phys. 34, 135 (1973).
  6. R. P. A. C. Newman, Strengths of naked singularities in Tolman-Bondi space-times, Classical Quantum Gravity 3, 527 (1986).
  7. B. C. Nolan, Strengths of singularities in spherical symmetry, Phys. Rev. D 60, 024014 (1999).
  8. C. Hellaby and K. Lake, Shell crossings and the Tolman model, Astrophys. J. 290, 381 (1985).
  9. K. Lake, The big bang in the Tolman models, Phys. Rev. D 29, 771 (1984).
  10. A. Papapetrou, Shock waves in the Newman-Penrose formalism, Commun. Math. Phys. 34, 229 (1973).
  11. C. J. S. Clarke and N. O’Donnell, Dynamical extension through a space-time singularity, Rend. Sem Mat. Univ. Politec. Torino 50, 39 (1992).
  12. J. Frauendiener and C. Klein, On crossing dust shells, J. Math. Phys. 36, 3632 (1995).
  13. B. C. Nolan, Dynamical extensions for shell crossing singularities, Classical Quantum Gravity 20, 575 (2003).
  14. B. Nolan, Singularity strengths and extendibility, Conf. Proc. C 0405132, 113 (2004).
  15. B. K. Tippett and I. Booth, Closest safe approach to an accreting black hole, Phys. Rev. D 90, 084027 (2014).
  16. W. Israel, Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B 44, 1 (1966); 48, 463(E) (1967).
  17. W. Israel, Gravitational collapse and causality, Phys. Rev. 153, 1388 (1967).
  18. E. Poisson, A Relativist’s Toolkit: The Mathematics of Black-Hole Mechanics (Cambridge University Press, Cambridge, UK, 2009).
  19. A. Papapetrou and A. Hamoui, Surfaces caustiques dégénérées dans la solution de Tolman. La singularité physique en relativité générale, Ann. Inst. Henri Poincaré Sect. A Phys. Théor. 6, 343 (1967).
  20. R. J. LeVeque, Finite-Volume Methods for Hyperbolic Problems (Cambridge University Press, Cambridge, UK, 2002).
  21. R. J. LeVeque, Numerical Methods for Conservation Laws, Lectures in Mathematics, 2nd ed. (Birkhäuser, Boston, 1992).
  22. P. D. Lasky, A. W. C. Lun, and R. B. Burston, Initial value formalism for dust collapse, ANZIAM 106, 53 (2006).
  23. V. Husain and T. Pawlowski, Time and a physical Hamiltonian for quantum gravity, Phys. Rev. Lett. 108, 141301 (2012).
  24. K. V. Kuchar, Geometrodynamics of Schwarzschild black holes, Phys. Rev. D 50, 3961 (1994) .
  25. C. W. Misner and D. H. Sharp, Relativistic equations for adiabatic, spherically symmetric gravitational collapse, Phys. Rev. 136, B571 (1964).
  26. F. Fazzini, V. Husain, and E. Wilson-Ewing, Shell-crossings and shock formation during gravitational collapse in effective loop quantum gravity, Phys. Rev. D 109, 084052 (2024).
  27. C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Grundlehren der mathematischen Wissenschaften: A Series of Comprehensive Studies in Mathematics, 3rd ed. (Springer, Dordrecht, 2010).
  28. J. F. Colombeau, Multiplication of Distributions. A Tool in Mathematics, Numerical Engineering and Theoretical Physics, Lecture Notes in Mathematics (Springer, Berlin, 1992), Vol. 1532.
  29. V. Husain and O. Winkler, Flat slice Hamiltonian formalism for dynamical black holes, Phys. Rev. D 71, 104001 (2005).
  30. V. Husain, J. G. Kelly, R. Santacruz, and E. Wilson-Ewing, Quantum gravity of dust collapse: Shock waves from black holes, Phys. Rev. Lett. 128, 121301 (2022).
  31. V. Husain, J. G. Kelly, R. Santacruz, and E. Wilson-Ewing, Fate of quantum black holes, Phys. Rev. D 106, 024014 (2022).
  32. H. Liu and D. Qu, Quantum induced shock dynamics in gravitational collapse: Insights from effective models and numerical frameworks, arXiv:2504.18462 [gr-qc].

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Phys. Rev. Research 7, 033215– Published 3 September, 2025
  • Received 29 April 2025
  • Accepted 4 August 2025
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