Complete solutions to the metric of spherically collapsing dust in an expanding spacetime with a cosmological constant

General Relativity and Gravitation

Volumn 44, Issue 10, 2012, Pages 2449-2476

  Valkenburg, Wessel ^a,b  

^a UNIVERSITEIT LEIDEN   (Netherlands)

^b INSTITUT FÜR THEORETISCHE PHYSIK   (Germany)

Author keywords

Cosmological constant; Lema tre Tolman Bondi; Spherical collapse

Indexed keywords

EID: 84865747961     PISSN: 00017701     EISSN: 15729532     Source Type: Journal    
DOI: 10.1007/s10714-012-1405-9     Document Type: Article

References (74)

1. Friedman, A.: Über die krümmung des raumes. Zeitschrift für Physik A Hadrons and Nuclei, 10, 377-386 (1922). ISSN 0939-7922. http://dx. doi. org/10. 1007/BF01332580. Reprinted in Gen. Relativ. Gravit. 31, 1985 (1999).
2. Friedmann, A: On the Possibility of a world with constant negative curvature of space. Z. Phys. 21, 326-332 (1924). doi: 10. 1007/BF01328280. Reprinted in Gen. Relativ. Gravit. 31, 1985 (1999).
3. Lemaître G.: Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques. Annales de la Societe Scietifique de Bruxelles 47, 49-59 (1927).
4. Robertson H. P.: Relativistic cosmology. Rev. Modern Phys. 5, 62-90 (1933). doi: 10. 1103/RevModPhys. 5. 62.
5. Walker A. G.: On Riemanntan spaces with spherical symmetry about a line, and the conditions for isotropy in genj relativity. Q. J. Math. 6, 81-93 (1935). doi: 10. 1093/qmath/os-6. 1. 81.
6. Lemaître, G.: L'Univers en expansion. Annales de la Societe Scietifique de Bruxelles, 53, 51 (1933). Reprinted in Gen. Relativ. Gravit. 29, 637 (1997).
7. Tolman, R. C.: Effect of inhomogeneity on cosmological models. Proc. Nat. Acad. Sci., 20, 169-176 (1934). Reprinted in Gen. Relativ. Gravit. 29, 931 (1997).
8. Bondi, H.: Spherically symmetrical models in general relativity. Mon. Not. R. Astron. Soc. 107, 410-425 (1947). Reprinted in Gen. Relativ. Gravit. 31, 1777 (1999).
9. van Acoleyen K.: LTB solutions in Newtonian gauge: from strong to weak fields. JCAP 0810, 028 (2008). doi: 10. 1088/1475-7516/2008/10/028.
10. Gunn J. E., Richard Gott J. III: On the infall of matter into cluster of galaxies and some effects on their evolution. Astrophys. J. 176, 1-19 (1972). doi: 10. 1086/151605.
11. Lahav O., Lilje P. B., Primack J. R., Rees M. J.: Dynamical effects of the cosmological constant. Mon. Not. R. Astron. Soc. 251, 128-136 (1991).
12. Jhingan S., Joshi P. S., Singh T. P.: The final fate of spherical inhomogeneous dust collapse II: initial data and causal structure of singularity. Class. Quant. Grav. 13, 3057-3068 (1996). doi: 10. 1088/0264-9381/13/11/019.
13. Wang L.-M., Steinhardt P. J.: Cluster abundance constraints on quintessence models. Astrophys. J. 508, 483-490 (1998). doi: 10. 1086/306436.
14. Sheth R. K., Mo H. J., Tormen G.: Ellipsoidal collapse and an improved model for the number and spatial distribution of dark matter haloes. Mon. Not. R. Astron. Soc. 323, 1 (2001). doi: 10. 1046/j. 1365-8711. 2001. 04006. x.
15. Deshingkar S. S., Chamorro A., Jhingan S., Joshi P. S.: Gravitational collapse and cosmological constant. Phys. Rev. D 63, 124005 (2001). doi: 10. 1103/PhysRevD. 63. 124005.
16. Krasinski A., Hellaby C.: Structure formation in the Lemaitre-Tolman model I. Phys. Rev. D 65, 023501 (2002). doi: 10. 1103/PhysRevD. 65. 023501.
17. Krasinski A., Hellaby C.: Formation of a galaxy with a central black hole in the Lemaitre-Tolman model. Phys. Rev. D 69, 043502 (2004). doi: 10. 1103/PhysRevD. 69. 043502.
18. Krasinski A., Hellaby C.: More examples of structure formation in the Lemaitre-Tolman model. Phys. Rev. D 69, 023502 (2004). doi: 10. 1103/PhysRevD. 69. 023502.
19. Mota D. F., van de Bruck C.: On the spherical collapse model in dark energy cosmologies. Astron. Astrophys. 421, 71-81 (2004). doi: 10. 1051/0004-6361: 20041090.
20. Bartelmann M., Doran M., Wetterich C.: Non-linear structure formation in cosmologies with early dark energy. Astron. Astrophys. 454, 27-36 (2006). doi: 10. 1051/0004-6361: 20053922.
21. Bolejko K., Hellaby C.: The great attractor and the shapley concentration. Gen. Relativ. Gravit. 40, 1771-1790 (2008). doi: 10. 1007/s10714-007-0573-5.
22. Firouzjaee J. T., Mansouri R.: Asymptotically FRW black holes. Gen. Relativ. Gravit. 42, 2431-2452 (2010). doi: 10. 1007/s10714-010-0991-7.
23. Bjaelde, O. E., Wong, Y. Y. Y.: Spherical collapse of dark energy with an arbitrary sound speed. (2010).
24. Firouzjaee, J. T.: The spherical symmetry Black hole collapse in expanding universe. (2011).
25. Sheth R. K., van de Weygaert R.: A hierarchy of voids: Much ado about nothing. Mon. Not. R. Astron. Soc. 350, 517 (2004). doi: 10. 1111/j. 1365-2966. 2004. 07661. x.
26. Bolejko K., Krasinski A., Hellaby C.: Formation of voids in the Universe within the Lemaitre-Tolman model. Mon. Not. R. Astron. Soc. 362, 213-228 (2005). doi: 10. 1111/j. 1365-2966. 2005. 09292. x.
27. Martino, M. C., Sheth, R. K.: Density profiles and voids in modified gravity models. (2009).
28. Biswas R., Alizadeh E., Wandelt B. D.: Voids as a precision probe of dark energy. Phys. Rev. D 82, 023002 (2010). doi: 10. 1103/PhysRevD. 82. 023002.
29. Moffat J. W., Tatarski D. C.: Redshift and structure formation in a spatially flat inhomogeneous universe. Phys. Rev. D 45(10), 3512-3522 (1992). doi: 10. 1103/PhysRevD. 45. 3512.
30. Moffat, J. W., Tatarski, D. C.: Cosmological observations in a local void. Astrophys. J. 453, 17 (1995) doi: 10. 1086/176365.
31. Tomita K.: Distances and lensing in cosmological void models. Astrophys. J. 529, 38 (2000). doi: 10. 1086/308277.
32. Tomita K.: Analyses of type Ia supernova data in cosmological models with a local void. Prog. Theor. Phys. 106, 929-939 (2001). doi: 10. 1143/PTP. 106. 929.
33. Moffat J. W.: Late-time inhomogeneity and acceleration without dark energy. JCAP 0605, 001 (2006). doi: 10. 1088/1475-7516/2006/05/001.
34. Mansouri, R.: Structured FRW universe leads to acceleration: a non-perturbative approach (2005).
35. Alnes H., Amarzguioui M., Gron O.: An inhomogeneous alternative to dark energy?. Phys. Rev. D 73, 083519 (2006). doi: 10. 1103/PhysRevD. 73. 083519.
36. Moffat J. W.: Cosmic microwave background, accelerating universe and inhomogeneous cosmology. JCAP 0510, 012 (2005). doi: 10. 1088/1475-7516/2005/10/012.
37. Enqvist K.: Mattsson Teppo the effect of inhomogeneous expansion on the supernova observations. JCAP 0702, 019 (2007). doi: 10. 1088/1475-7516/2007/02/019.
38. Chung D. J. H., Romano A. E.: Mapping luminosity-redshift relationship to LTB Cosmology. Phys. Rev. D 74, 103507 (2006). doi: 10. 1103/PhysRevD. 74. 103507.
39. Enqvist K.: Lemaitre-Tolman-Bondi model and accelerating expansion. Gen. Relativ. Gravit. 40, 451-466 (2008). doi: 10. 1007/s10714-007-0553-9.
40. Garcia-Bellido J., Haugboelle T.: Confronting Lemaitre-Tolman-Bondi models with observational cosmology. JCAP 0804, 003 (2008). doi: 10. 1088/1475-7516/2008/04/003.
41. Zibin, J. P., Moss, A., Scott, D.: Can we avoid dark energy? Phys. Rev. Lett. 101, 251303 (2008). doi: 10. 1103/PhysRevLett. 101. 251303.
42. Romano, A. E.: Can the cosmological constant be mimicked by smooth large-scale inhomogeneities for more than one observable? JCAP 1005, 020 (2010). doi: 10. 1088/1475-7516/2010/05/020.
43. Clifton T., Ferreira P. G., Zuntz J.: What the small angle CMB really tells us about the curvature of the universe. JCAP 0907, 029 (2009). doi: 10. 1088/1475-7516/2009/07/029.
44. February S., Larena J., Smith M., Clarkson C.: Rendering dark energy void. Mon. Not. R. Astron. Soc. 405, 2231 (2010).
45. Sollerman J. et al.: First-year sloan digital sky survey-II (SDSS-II) supernova results: constraints on non-standard cosmological models. Astrophys. J. 703, 1374-1385 (2009). doi: 10. 1088/0004-637X/703/2/1374.
46. Yoo C.-M., Nakao K.I., Sasaki M.: CMB observations in LTB universes: part II: the kSZ effect in an LTB universe. JCAP 1010, 011 (2010). doi: 10. 1088/1475-7516/2010/10/011.
47. Clarkson C., Regis M.: The cosmic microwave background in an inhomogeneous universe-why void models of dark energy are only weakly constrained by the CMB. JCAP 1102, 013 (2011). doi: 10. 1088/1475-7516/2011/02/013.
48. Marra V., Paakkonen M.: Observational constraints on the LLTB model. JCAP 1012, 021 (2010). doi: 10. 1088/1475-7516/2010/12/021.
49. Amendola L., Kainulainen K., Marra V., Quartin M.: Large-scale inhomogeneities may improve the cosmic concordance of supernovae. Phys. Rev. Lett. 105, 121302 (2010). doi: 10. 1103/PhysRevLett. 105. 121302.
50. Biswas T., Notari A., Valkenburg W.: Testing the void against cosmological data: fitting CMB, BAO, SN and H0. JCAP 1011, 030 (2010). doi: 10. 1088/1475-7516/2010/11/030.
51. Nadathur S., Sarkar S.: Reconciling the local void with the CMB. Phys. Rev. D 83, 063506 (2011). doi: 10. 1103/PhysRevD. 83. 063506.
52. Alonso D., Garcia-Bellido J., Haugbolle T., Vicente J.: Large scale structure simulations of inhomogeneous LTB void models. Phys. Rev. D 82, 123530 (2010). doi: 10. 1103/PhysRevD. 82. 123530.
53. Sinclair B., Davis T. M., Haugbolle T.: Residual hubble-bubble effects on supernova cosmology. Astrophys. J. 718, 1445-1455 (2010). doi: 10. 1088/0004-637X/718/2/1445.
54. Marra, V., Notari, A.: Observational constraints on inhomogeneous cosmological models without dark energy (2011).
55. Marra V., Kolb E. W., Matarrese S., Riotto A.: On cosmological observables in a swiss-cheese universe. Phys. Rev. D 76, 123004 (2007). doi: 10. 1103/PhysRevD. 76. 123004.
56. Biswas T., Notari A.: Swiss-Cheese inhomogeneous cosmology & the dark energy problem. JCAP 0806, 021 (2008). doi: 10. 1088/1475-7516/2008/06/021.
57. Valkenburg W.: Swiss Cheese and a Cheesy CMB. JCAP 0906, 010 (2009). doi: 10. 1088/1475-7516/2009/06/010.
58. Kessler R. et al.: First-year sloan digital sky survey-II (SDSS-II) supernova results: hubble diagram and cosmological parameters. Astrophys. J. Suppl. 185, 32-84 (2009). doi: 10. 1088/0067-0049/185/1/32.
59. Reid B. A. et al.: Baryon acoustic oscillations in the sloan digital sky survey data release 7 galaxy sample. Mon. Not. R. Astron. Soc. 401, 2148-2168 (2010). doi: 10. 1111/j. 1365-2966. 2009. 15812. x.
60. Komatsu E. et al.: Seven-year wilkinson microwave anisotropy probe (WMAP) observations: cosmological interpretation. Astrophys. J. Suppl. 192, 18 (2011). doi: 10. 1088/0067-0049/192/2/18.
61. Sandage A. et al.: The hubble constant: a summary of the HST program for the luminosity calibration of type Ia supernovae by means of cepheids. Astrophys. J. 653, 843-860 (2006). doi: 10. 1086/508853.
62. Romano, A. E., Sasaki, M., Starobinsky, A. A.: Effects of inhomogeneities on apparent cosmological observables: "fake" evolving dark energy (2010).
63. Romano, A. E., Chen, P.: Corrections to the apparent value of the cosmological constant due to local inhomogeneities (2011).
64. Omer G. C.: Spherically symmetric distributions of matter without pressure. Proc. Natl. Acad. Sci. 53, 1-5 (1965). doi: 10. 1073/pnas. 53. 1. 1.
65. Ruban, V. A.: Spherically symmetric T-models in the general theory of relativity. Sov. J. Exp. Theor. Phys. 29, 1027 (1969).
66. Barrow J. D., Stein-Schabes J.: Inhomogeneous cosmologies with cosmological constant. Phys. Lett. A103, 315 (1984). doi: 10. 1016/0375-9601(84)90467-5.
67. Krasinski, A.: Inhomogeneous cosmological models.
68. Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C., Herlt, E.: Exact solutions of Einstein's field equations. (2003).
69. Alexander S., Biswas T., Notari A., Vaid D.: Local void vs dark energy: confrontation with WMAP and type Ia supernovae. JCAP 0909, 025 (2009). doi: 10. 1088/1475-7516/2009/09/025.
70. Carlson, B. C.: In digital library of mathematical functions. National Institute of Standards and Technology from http://dlmf. nist. gov/, 2010-05-07.
71. Carlson B. C.: Numerical computation of real or complex elliptic integrals. Numer. Algor. 10, 13-26 (1995). doi: 10. 1007/BF02198293.
72. Bolejko, K., Hellaby, C., Alfedeel, A. H. A.: The metric of the cosmos from luminosity and age data (2011).
73. Carlson, B. C.: Elliptic integrals: symmetry and symbolic integration. Atti dei Convegni Lincei 147, 161-181 (1998) http://www. osti. gov/bridge/product. biblio. jsp?osti_id=348931.
74. Carlson, B. C.: Toward symbolic integration of elliptic integrals. J. Symbol. Comput. 28(6), 739-753 (1999). ISSN 0747-7171. doi: 10. 1006/jsco. 1999. 0336. http://www. sciencedirect. com/science/article/B6WM7-45FKTYR-1J/2/c4899e983e4f3e2b1103ea95eceacb00.