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Symmetry and instability of marginally outer trapped surfaces

Published 3 Nov 2023 in gr-qc and math.DG | (2311.02063v2)

Abstract: We consider an initial data set having a continuous symmetry and a marginally outer trapped surface (MOTS) that is not preserved by this symmetry. We show that such a MOTS is unstable except in an exceptional case. In non-rotating cases we provide a Courant-type lower bound on the number of unstable eigenvalues. These results are then used to prove the instability of a large class of exotic MOTSs that were recently observed in the Schwarzschild spacetime. We also discuss the implications for the apparent horizon in data sets with translational symmetry.

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References (46)
  1. The time evolution of marginally trapped surfaces. Class. Quant. Grav., 26:085018, 2009.
  2. Local existence of dynamical and trapping horizons. Phys. Rev. Lett., 95:111102, 2005.
  3. Stability of marginally outer trapped surfaces and existence of marginally outer trapped tubes. Adv. Theor. Math. Phys., 12(4):853–888, 2008.
  4. L. Andersson and J. Metzger. The area of horizons and the trapped region. Comm. Math. Phys., 290(3):941–972, 2009.
  5. A. Ashtekar and G. J. Galloway. Some uniqueness results for dynamical horizons. Adv. Theor. Math. Phys., 9(1):1–30, 2005.
  6. R. Beig and P. T. Chrusciel. Killing initial data. Classical and Quantum Gravity, 14(1A):A83, jan 1997.
  7. I. Ben-Dov. The Penrose inequality and apparent horizons. Phys. Rev. D, 70:124031, 2004.
  8. I. Bengtsson and J. M. M. Senovilla. The Region with trapped surfaces in spherical symmetry, its core, and their boundaries. Phys. Rev. D, 83:044012, 2011.
  9. Marginally trapped tubes and dynamical horizons. Class. Quant. Grav., 23:413–440, 2006.
  10. Exotic marginally outer trapped surfaces in rotating spacetimes of any dimension. Class. Quant. Grav., 40(9):095010, 2023.
  11. I. Booth and S. Fairhurst. Isolated, slowly evolving, and dynamical trapping horizons: Geometry and mechanics from surface deformations. Phys. Rev. D, 75:084019, 2007.
  12. Marginally outer trapped surfaces in the Schwarzschild spacetime: Multiple self-intersections and extreme mass ratio mergers. Phys. Rev. D, 102(4):044031, 2020.
  13. Ultimate fate of apparent horizons during a binary black hole merger. I. Locating and understanding axisymmetric marginally outer trapped surfaces. Phys. Rev. D, 104(8):084083, 2021.
  14. Unstable marginally outer trapped surfaces in static spherically symmetric spacetimes. Phys. Rev. D, 96(2):024059, 11, 2017.
  15. Eigenvalues of the MOTS stability operator for slowly rotating Kerr black holes. Gen. Relativity Gravitation, 53(1):Paper No. 16, 14, 2021.
  16. L.-M. Cao. Deformation of Codimension-2 Surface and Horizon Thermodynamics. JHEP, 03:112, 2011.
  17. A. Carrasco and M. Mars. Stability of marginally outer trapped surfaces and symmetries. Classical Quantum Gravity, 26(17):175002, 19, 2009.
  18. Horizon dynamics of distorted rotating black holes. Phys. Rev. D, 83:104018, 2011.
  19. A. Coley and D. McNutt. Identification of black hole horizons using scalar curvature invariants. Class. Quant. Grav., 35(2):025013, 2018.
  20. New examples of marginally trapped surfaces and tubes in warped spacetimes. Classical and Quantum Gravity, 27(14):145021, jun 2010.
  21. Dynamics of marginally trapped surfaces in a binary black hole merger: Growth and approach to equilibrium. Phys. Rev. D, 97(8):084028, 2018.
  22. P. Hájiček. Three remarks on axisymmetric stationary horizons. Commun. Math. Phys., 36(4):305–320, 1974.
  23. S. W. Hawking. The event horizon. In Les Houches Summer School of Theoretical Physics: Black Holes, pages 1–56, 1973.
  24. The Large Scale Structure of Space-Time. Cambridge Monographs on Mathematical Physics. Cambridge University Press, 1973.
  25. S. A. Hayward. General laws of black hole dynamics. Phys. Rev. D, 49:6467–6474, 1994.
  26. Interior marginally outer trapped surfaces of spherically symmetric black holes. Phys. Rev. D, 105(4):044024, 2022.
  27. E. Jakobsson. How trapped surfaces jump in 2+1 dimensions. Class. Quant. Grav., 30:065022, 2013.
  28. J. L. Jaramillo. An introduction to local Black Hole horizons in the 3+1 approach to General Relativity. Int. J. Mod. Phys. D, 20:2169, 2011.
  29. J. L. Jaramillo. A perspective on Black Hole Horizons from the Quantum Charged Particle. J. Phys. Conf. Ser., 600(1):012037, 2015.
  30. J. L. Jaramillo. Black hole horizons and quantum charged particles. Classical Quantum Gravity, 32(13):132001, 9, 2015.
  31. Toroidal trapped surfaces and isoperimetric inequalities. Phys. Rev. D, 95(6):064037, 2017.
  32. S. Kobayashi. Fixed points of isometries. Nagoya Math. J., 13:63–68, 1958.
  33. M. Kriele and S. A. Hayward. Outer trapped surfaces and their apparent horizon. J. Math. Phys., 38(3):1593–1604, 1997.
  34. P. Mach and N. Xie. Toroidal marginally outer trapped surfaces in closed Friedmann-Lemaître-Robertson-Walker spacetimes: Stability and isoperimetric inequalities. Phys. Rev. D, 96(8):084050, 2017.
  35. M. Mars and J. M. M. Senovilla. Trapped surfaces and symmetries. Classical and Quantum Gravity, 20(24):L293, nov 2003.
  36. R. P. A. C. Newman. Topology and stability of marginal 2-surfaces. Classical and Quantum Gravity, 4(2):277, mar 1987.
  37. The Slicing dependence of non-spherically symmetric quasi-local horizons in Vaidya Spacetimes. Phys. Rev. D, 83:124022, 2011.
  38. D. Pook-Kolb. Dynamical Horizons in Binary Black Hole Mergers. PhD thesis, Gottfried Wilhelm Leibniz Universität, Hannover, 2020. Available at https://www.repo.uni-hannover.de/handle/123456789/10206.
  39. Horizons in a binary black hole merger II: Fluxes, multipole moments and stability. 6 2020.
  40. Interior of a Binary Black Hole Merger. Phys. Rev. Lett., 123(17):171102, 2019.
  41. Self-intersecting marginally outer trapped surfaces. Phys. Rev. D, 100(8):084044, 2019.
  42. Ultimate fate of apparent horizons during a binary black hole merger. II. The vanishing of apparent horizons. Phys. Rev. D, 104(8):084084, 2021.
  43. What Happens to Apparent Horizons in a Binary Black Hole Merger? Phys. Rev. Lett., 127(18):181101, 2021.
  44. Introduction to dynamical horizons in numerical relativity. Phys. Rev. D, 74:024028, 2006.
  45. J. Thornburg. Event and apparent horizon finders for 3+1 numerical relativity. Living Rev. Rel., 10:3, 2007.
  46. R. M. Wald. General relativity. University of Chicago Press, Chicago, IL, 1984.
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