Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 83 tok/s
Gemini 2.5 Pro 49 tok/s Pro
GPT-5 Medium 16 tok/s Pro
GPT-5 High 15 tok/s Pro
GPT-4o 109 tok/s Pro
Kimi K2 181 tok/s Pro
GPT OSS 120B 468 tok/s Pro
Claude Sonnet 4 36 tok/s Pro
2000 character limit reached

Apparent horizon tracking in supercritical solutions of the Einstein-scalar field equations in spherical symmetry in affine-null coordinates (2405.19122v2)

Published 29 May 2024 in gr-qc and hep-th

Abstract: Choptuik's critical phenomena in general relativity is revisited in the affine-null metric formulation of Einstein's equations for a massless scalar field in spherical symmetry. Numerical solutions are obtained by evolution of initial data using pseudo-spectral methods. The underlying system consists of differential equations along the outgoing null rays which can be solved in sequential form. A new two-parameter family of initial data is presented for which these equations can be integrated analytically. Specific choices of the initial data parameters correspond to either an asymptotically flat null cone, a black hole event horizon or the singular interior of a black hole. Our main focus is on the interior features of a black hole, for which the affine-null system is especially well adapted. We present both analytic and numerical results describing the geometric properties of the apparent horizon and final singularity. Using a re-gridding technique for the affine parameter, numerical evolution of initially asymptotically flat supercritical data can be continued inside the event horizon and track the apparent horizon up to the formation of the final singularity.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (32)
  1. M. W. Choptuik, “Universality and scaling in gravitational collapse of a massless scalar field,” Phys. Rev. Lett. , vol. 70, pp. 9–12, Jan. 1993.
  2. C. Gundlach, “Choptuik Spacetime as an Eigenvalue Problem,” Phys. Rev. Lett. , vol. 75, pp. 3214–3217, Oct. 1995.
  3. S. Hod and T. Piran, “Critical behavior and universality in gravitational collapse of a charged scalar field,” Phys. Rev. D, vol. 55, pp. 3485–3496, Mar. 1997.
  4. R. S. Hamadé and J. M. Stewart, “The spherically symmetric collapse of a massless scalar field,” Classical and Quantum Gravity, vol. 13, pp. 497–512, Mar. 1996.
  5. M. Reiterer and E. Trubowitz, “Choptuik’s Critical Spacetime Exists,” Communications in Mathematical Physics, vol. 368, pp. 143–186, May 2019.
  6. C. Gundlach, “Understanding critical collapse of a scalar field,” Phys. Rev. D, vol. 55, pp. 695–713, Jan. 1997.
  7. E. W. Hirschmann and D. M. Eardley, “Universal scaling and echoing in the gravitational collapse of a complex scalar field,” Phys. Rev. D, vol. 51, pp. 4198–4207, Apr. 1995.
  8. C. Gundlach and J. M. Martín-García, “Critical Phenomena in Gravitational Collapse,” Living Reviews in Relativity, vol. 10, p. 5, Dec. 2007.
  9. J. M. Martín-García and C. Gundlach, “Global structure of Choptuik’s critical solution in scalar field collapse,” Phys. Rev. D, vol. 68, p. 024011, July 2003.
  10. D. Garfinkle, “Choptuik scaling in null coordinates,” Phys. Rev. D, vol. 51, pp. 5558–5561, 1995.
  11. M. Purrer, S. Husa, and P. C. Aichelburg, “News from critical collapse: Bondi mass, tails and quasinormal modes,” Phys. Rev. D, vol. 71, p. 104005, 2005.
  12. J. A. Crespo, H. P. de Oliveira, and J. Winicour, “Affine-null formulation of the gravitational equations: Spherical case,” Phys. Rev. D, vol. 100, p. 104017, Nov. 2019.
  13. C. Lechner, J. Thornburg, S. Husa, and P. C. Aichelburg, “New transition between discrete and continuous self-similarity in critical gravitational collapse,” Phys. Rev. D, vol. 65, p. 081501, Apr. 2002.
  14. J. Winicour, “Affine-null metric formulation of Einstein’s equations,” Phys. Rev. D, vol. 87, p. 124027, June 2013.
  15. J. Winicour, “Characteristic Evolution and Matching,” Living Reviews in Relativity, vol. 15, p. 2, Jan. 2012.
  16. C. J. Handmer and B. Szilágyi, “Spectral characteristic evolution: a new algorithm for gravitational wave propagation,” Classical and Quantum Gravity, vol. 32, p. 025008, Jan. 2015.
  17. C. J. Handmer, B. Szilágyi, and J. Winicour, “Spectral Cauchy characteristic extraction of strain, news and gravitational radiation flux,” Classical and Quantum Gravity, vol. 33, p. 225007, Nov. 2016.
  18. T. Mädler, “Affine-null metric formulation of general relativity at two intersecting null hypersurfaces,” Phys. Rev. D, vol. 99, p. 104048, May 2019.
  19. T. Mädler and E. Gallo, “Slowly rotating Kerr metric derived from the Einstein equations in affine-null coordinates,” Phys. Rev. D, vol. 107, p. 104010, May 2023.
  20. E. Gallo, C. Kozameh, T. Mädler, O. M. Moreschi, and A. Perez, “Spherically symmetric black holes and affine-null metric formulation of Einstein’s equations,” Phys. Rev. D, vol. 104, p. 084048, Oct. 2021.
  21. T. Mädler and E. Müller, “The Bondi-Sachs metric at the vertex of a null cone: axially symmetric vacuum solutions,” Classical and Quantum Gravity, vol. 30, p. 055019, Mar. 2013.
  22. H. Bondi, M. G. J. van der Burg, and A. W. K. Metzner, “Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems,” Proceedings of the Royal Society of London Series A, vol. 269, pp. 21–52, Aug. 1962.
  23. L. A. Tamburino and J. H. Winicour, “Gravitational Fields in Finite and Conformal Bondi Frames,” Physical Review, vol. 150, pp. 1039–1053, Oct. 1966.
  24. T. Mädler and J. Winicour, “The sky pattern of the linearized gravitational memory effect,” Classical and Quantum Gravity, vol. 33, p. 175006, Sept. 2016.
  25. “Anaconda software distribution,” 2020.
  26. S. K. Lam, A. Pitrou, and S. Seibert, “Numba: A llvm-based python jit compiler,” in Proceedings of the Second Workshop on the LLVM Compiler Infrastructure in HPC, pp. 1–6, 2015.
  27. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey, İ. Polat, Y. Feng, E. W. Moore, J. VanderPlas, D. Laxalde, J. Perktold, R. Cimrman, I. Henriksen, E. A. Quintero, C. R. Harris, A. M. Archibald, A. H. Ribeiro, F. Pedregosa, P. van Mulbregt, and SciPy 1.0 Contributors, “SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python,” Nature Methods, vol. 17, pp. 261–272, 2020.
  28. S. Olver and A. Townsend, “A fast and well-conditioned spectral method,” SIAM Review, vol. 55, no. 3, pp. 462–489, 2013.
  29. S. Olver, R. M. Slevinsky, and A. Townsend, “Fast algorithms using orthogonal polynomials,” Acta Numerica, vol. 29, p. 573–699, 2020.
  30. C.-W. Shu and S. Osher, “Efficient Implementation of Essentially Non-oscillatory Shock-Capturing Schemes,” Journal of Computational Physics, vol. 77, pp. 439–471, Aug. 1988.
  31. Cambridge University Press, 2007.
  32. T. Mädler and J. Winicour, “Bondi-Sachs Formalism,” Scholarpedia, vol. 11, p. 33528, Dec. 2016.
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Ai Generate Text Spark Streamline Icon: https://streamlinehq.com

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

List Streamline Icon: https://streamlinehq.com Explore 10 Community Prompts
Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets