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A dynamical systems formulation for inhomogeneous LRS-II spacetimes

Published 1 Apr 2024 in gr-qc | (2404.01161v3)

Abstract: We present a dynamical system formulation for inhomogeneous LRS-II spacetimes using the covariant 1+1+2 decomposition approach. Our approach describes the LRS-II dynamics from the point of view of a comoving observer. Promoting the covariant radial derivatives of the covariant dynamical quantities to new dynamical variables and utilizing the commutation relation between the covariant temporal and radial derivatives, we were able to construct an autonomous system of first-order ordinary differential equations along with some purely algebraic constraints. Using our dynamical system formulation we found several interesting features in the LRS-II phase space with dust, one of them being that the homogeneous solutions constitute an invariant submanifold. For the particular case of LTB, we were also able to recover the previously known result that an expanding LTB tends to Milne in the absence of a cosmological constant, providing a potential validation of our formalism.

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References (60)
  1. Relativistic cosmology and large-scale structure. Phys. Rept., 465:61–147, 2008.
  2. Steven Weinberg. The Cosmological Constant Problem. Rev. Mod. Phys., 61:1–23, 1989.
  3. Eleonora Di Valentino et al. Snowmass2021 - Letter of interest cosmology intertwined II: The hubble constant tension. Astropart. Phys., 131:102605, 2021.
  4. Eleonora Di Valentino et al. Cosmology Intertwined III: f⁢σ8𝑓subscript𝜎8f\sigma_{8}italic_f italic_σ start_POSTSUBSCRIPT 8 end_POSTSUBSCRIPT and S8subscript𝑆8S_{8}italic_S start_POSTSUBSCRIPT 8 end_POSTSUBSCRIPT. Astropart. Phys., 131:102604, 2021.
  5. Dynamics of dark energy. Int. J. Mod. Phys. D, 15:1753–1936, 2006.
  6. Dark Energy: Theory and Observations. Cambridge University Press, 2010.
  7. E. Papantonopoulos. Modifications of Einstein’s Theory of Gravity at Large Distances. Lecture Notes in Physics. Springer International Publishing, 2014.
  8. Yashar Akrami et al. Modified Gravity and Cosmology: An Update by the CANTATA Network. Springer, 2021.
  9. Dynamical systems applied to cosmology: dark energy and modified gravity. Phys. Rept., 775-777:1–122, 2018.
  10. Accelerating universe via spatial averaging. 7 2005.
  11. John W. Moffat. Late-time inhomogeneity and acceleration without dark energy. JCAP, 05:001, 2006.
  12. Cosmological acceleration and gravitational collapse. JCAP, 06:009, 2006.
  13. Reza Mansouri. Structured frw universe leads to acceleration: a non-perturbative approach. 12 2005.
  14. Mimicking dark energy with Lemaitre-Tolman-Bondi models: Weak central singularities and critical points. Phys. Rev. D, 74:023506, 2006.
  15. An inhomogeneous alternative to dark energy? Phys. Rev. D, 73:083519, 2006.
  16. David Garfinkle. Inhomogeneous spacetimes as a dark energy model. Class. Quant. Grav., 23:4811–4818, 2006.
  17. Is dark energy the only solution to the apparent acceleration of the present universe? Prog. Theor. Phys., 108:809–818, 2002.
  18. Tension in the Void: Cosmic Rulers Strain Inhomogeneous Cosmologies. JCAP, 10:009, 2012.
  19. Observational constraints on inhomogeneous cosmological models without dark energy. Class. Quant. Grav., 28:164004, 2011.
  20. Leandros Perivolaropoulos. Large Scale Cosmological Anomalies and Inhomogeneous Dark Energy. Galaxies, 2:22–61, 2014.
  21. Large scale inhomogeneity versus source evolution: Can we distinguish them observationally? Mon. Not. Roy. Astron. Soc., 292:817–830, 1997.
  22. Pankaj S. Joshi. Gravitational collapse: The Story so far. Pramana, 55:529–544, 2000.
  23. Equilibrium configurations from gravitational collapse. Class. Quant. Grav., 28:235018, 2011.
  24. Daniele Malafarina. A Brief Review of Relativistic Gravitational Collapse. Astrophys. Space Sci. Libr., 440:169–197, 2016.
  25. Dynamical Systems in Cosmology. Cambridge University Press, 1997.
  26. Alan A. Coley. Dynamical systems in cosmology. In Spanish Relativity Meeting (ERE 99), 9 1999.
  27. Henk van Elst and Claes Uggla. General relativistic (1+3) orthonormal frame approach revisited. Class. Quant. Grav., 14:2673–2695, 1997.
  28. Dynamical systems approach to G(2) cosmology. Class. Quant. Grav., 19:51–82, 2002.
  29. The Past attractor in inhomogeneous cosmology. Phys. Rev. D, 68:103502, 2003.
  30. Asymptotic isotropization in inhomogeneous cosmology. Phys. Rev. D, 69:103507, 2004.
  31. Roberto A. Sussman. A Dynamical system approach to inhomogeneous dust solutions. Class. Quant. Grav., 25:015012, 2008.
  32. A Dynamical systems study of the inhomogeneous Lambda-CDM model. Class. Quant. Grav., 28:045006, 2011.
  33. Covariant perturbations of Schwarzschild black holes. Class. Quant. Grav., 20:3855–3884, 2003.
  34. Chris Clarkson. A Covariant approach for perturbations of rotationally symmetric spacetimes. Phys. Rev. D, 76:104034, 2007.
  35. J. Ehlers. Contributions to the relativistic mechanics of continuous media. Abh. Akad. Wiss. Lit. Mainz. Nat. Kl., 11:793–837, 1961.
  36. George F. R. Ellis and Henk van Elst. Cosmological models: Cargese lectures 1998. NATO Sci. Ser. C, 541:1–116, 1999.
  37. Global structure of black holes via the dynamical system. Class. Quant. Grav., 32(10):105006, 2015.
  38. Global structure of static spherically symmetric solutions surrounded by quintessence. Class. Quant. Grav., 34(12):125014, 2017.
  39. Solutions of Einstein’s equations for a fluid which exhibit local rotational symmetry. J. Math. Phys., 9:1072–1082, 1968.
  40. Scalar and electromagnetic perturbations on LRS class II space-times. Class. Quant. Grav., 21:5587–5608, 2004.
  41. Covariant perturbations of Schwarzschild black holes in f(R) gravity. Int. J. Mod. Phys. D, 26(06):1750048, 2016.
  42. A Geometrical Approach to Strong Gravitational Lensing in f(R) Gravity. Phys. Rev. D, 83:024030, 2011.
  43. A New framework for studying spherically symmetric static solutions in f(R) gravity. Phys. Rev. D, 81:084028, 2010.
  44. Rituparno Goswami and George F R Ellis. Almost Birkhoff Theorem in General Relativity. Gen. Rel. Grav., 43:2157–2170, 2011.
  45. New class of LRS spacetimes with simultaneous rotation and spatial twist. Phys. Rev. D, 94(10):104040, 2016.
  46. Spherically symmetric cosmology: Resource paper. 3 2008.
  47. The Dynamics of Lemaitre-Tolman cosmologies. Class. Quant. Grav., 26:085017, 2009.
  48. Rituparno Goswami and George F. R. Ellis. Birkhoff Theorem and Matter. Gen. Rel. Grav., 44:2037–2050, 2012.
  49. Naked singularities in spherically symmetric inhomogeneous Tolman-Bondi dust cloud collapse. Phys. Rev. D, 47:5357–5369, 1993.
  50. All black holes in Lemaître–Tolman–Bondi inhomogeneous dust collapse. Class. Quant. Grav., 32(14):145004, 2015.
  51. Pankaj S. Joshi. On the genericity of spacetime singularities. Pramana, 69:119–136, 2007.
  52. Why do naked singularities form in gravitational collapse? Phys. Rev. D, 65:101501, 2002.
  53. Why do naked singularities form in gravitational collapse? 2. Phys. Rev. D, 70:087502, 2004.
  54. Role of initial data in spherical collapse. Phys. Rev. D, 69:064027, 2004.
  55. How close can an Inhomogeneous Universe mimic the Concordance Model? JCAP, 06:017, 2010.
  56. James P. Zibin. Scalar Perturbations on Lemaitre-Tolman-Bondi Spacetimes. Phys. Rev. D, 78:043504, 2008.
  57. Inhomogeneity of the ΛΛ\Lambdaroman_ΛLTB models. 1 2016.
  58. Cosmic Censorship Conjecture revisited: Covariantly. Class. Quant. Grav., 31:135010, 2014.
  59. Cosmic censorship conjecture revisited: Covariantly. In 14th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories, volume 3, pages 2615–2620, 2017.
  60. Bounce behaviour in Kantowski-Sachs and Bianchi cosmologies. Class. Quant. Grav., 23:6585–6597, 2006.
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