Please wait a minute...
Chin. Phys. B, 2012, Vol. 21(6): 060401    DOI: 10.1088/1674-1056/21/6/060401
GENERAL Prev   Next  

Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity

Gamal G. L. Nasheda)b)c)†
a. Mathematics Department, Faculty of Science, King Faisal University, P. O. Box 380 Al-Ahsaa 31982,the Kingdom of Saudi Arabia;
b. Mathematics Department, Faculty of Science, Ain Shams University, Cairo, 11566, Egypt;
c. Center for Theoretical Physics, British University of Egypt, Sherouk City 11837, P. O. Box 43, Egypt
Abstract  A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity (TEGR). A spacetime which is not asymptotically flat is derived. The energy conditions of this spacetime are studied. It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy. The singularities of this solution are discussed.
Keywords:  perfect fluid with self-similarity of second kind      teleparallel equivalent of general relativity      asymptotically nonflat spacetime      energy conditions  
Received:  19 November 2011      Revised:  06 January 2012      Accepted manuscript online: 
PACS:  04.20.Jb (Exact solutions)  
  04.50.Kd (Modified theories of gravity)  
  04.30.-w (Gravitational waves)  
Corresponding Authors:  Gamal G. L. Nashed     E-mail:  nashed@bue.edu.eg

Cite this article: 

Gamal G. L. Nashed Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity 2012 Chin. Phys. B 21 060401

[1] Riess A G, Filippenko A V, Challis P, Clocchiatti A, Diercks A, Garnavich P M, Gilliland R L, Hogan C J, Jha S, Kirshner R P, Leibundgut B, Phillips M M, Reiss D, Schmidt B P, Schommer R A, Smith R C, Spyromilio J, Stubbs C, Suntzeff N B and Tonry J 1998 Astron. J. 116 1009
[2] Perlmutter S, Aldering G, Deustua S, Fabbro S, Goldhaber G, Groom D E, Kim A G, Kim M Y, Knop R A, Nugent P, Pennypacker C R, Goobar A, Pain R, Hook I M, Lidman C, Ellis R S, Irwin M, McMahon R G, Ruiz-Lapuente P, Walton N, Schaefer B, Boyle B J, Filippenko A V, Matheson T, Fruchter A S, Panagia N, Newberg H J M and Couch W J 1999 Astrophys. J. 517 565
[3] de Bernardis P, Ade P A R, Bock J J, Bond J R, Borrill J, Boscaleri A, Coble K, Crill B P, de Gasperis G, Farese P C, Ferreira P G, Ganga K, Giacometti M, Hivon E, Hristov V V, Iacoangeli A, Jaffe A H, Lange A E, Martinis L, Masi S, Mason P V, Mauskopf P D, Melchiorri A, Miglio L, Montroy T, Netterfield C B, Pascale E, Piacentini F, Pogosyan D, Prunet S, Rao S, Romeo G, Ruh J E, Scaramuzzi F, Sforna D and Vittorio N 2000 Nature 404 955
[4] Hanany S, Ade P, Balbi A, Bock J, Borrill J, Boscaleri A, de Bernardis P, Ferreira P G, Hristov V V, Jaffe A H, Lange A E, Lee A T, Mauskopf P D, Netterfield C B, Oh S, Pascale E, Rabii B, Richards P L, Smoot G F, Stompor R, Winant C D and Wu J H P 2000 Astrophys. J. 545 L5
[5] Peebles P J E and Ratra B 2003 Rev. Mod. Phys. 75 559
[6] Padmanabhan T 2003 Phys. Rep. 380 235
[7] Caldwell R R, Dave R and Steinhardt P J 1998 Phys. Rev. Lett. 80 1582
[8] Liddle A R and Scherrer R J 1999 Phys. Rev. D 59 023509
[9] Steinhardt P J, Wang L M and Zlatev I 1999 Phys. Rev. D 59 123504
[10] Dvali G R, Gabadadze G and Porrati M 2000 Phys. Lett. B 484 112
[11] Deffayet C 2001 Phys. Lett. B 502 199
[12] Capozziello S, Carloni S and Troisi A 2003 arXiv/: astro-ph/0303041
[13] Carroll S M, Duvvuri V, Trodden M and Turner M S 2003 Phys. Rev. D 70 043528
[14] Nojiri S and Odintsov S D 2003 Phys. Rev. D 68 123512
[15] Townsend P K and Wohlfarth N R 2003 Phys. Rev. Lett. 91 061302
[16] Gibbons G W 1985 Supersymmetry, Supergravity and Related Topics, eds. de Aguila F et al. (Singapore: World Scientific) p. 124
[17] Maldacena J M and Nuñez C 2001 Int. J. Mod. Phys. A 16 822
[18] Ohta N 2003 Phys. Rev. Lett. 91 061303
[19] Wohlfarth N R 2003 Phys. Lett. B 563 1
[20] Roy S 2003 Phys. Lett. B 567 322
[21] Webb J K, Murphy M T, Flambaum V V, Dzuba V A, Barrow J D, Churchill C W, Prochaska J X and Wolfe A M 2001 Phys. Rev. Lett. 87 091301
[22] Cline J M and Vinet J 2003 Phys. Rev. D 68 025015
[23] Ohta N 2003 Prog. Theor. Phys. 110 269
[24] Ohta N 2005 Int. J. Mod. Phys. A 20 1
[25] Chen C M, Ho P M, Neupane I P, Wang J E and Ohta N 2003 JHEP 10 058
[26] Bergshoeff E 2004 Class. Quantum Grav. 21 1947
[27] Gong Y and Wang A 2006 Class. Quantum Grav. 23 3419
[28] Neupane I P and Wiltshire D L 2005 Phys. Lett. B 619 201
[29] Neupane I P and Wiltshire D L 2005 Phys. Rev. D 72 083509
[30] Maeda K and Ohta N 2005 Phys. Rev. D 71 063520
[31] Neupane I P 2007 Phys. Rev. Lett. 98 061301
[32] Gong Y, Wang A and Wu Q 2008 Phys. Lett. B 663 147
[33] Pereira P R C T, da Silva M F A and Chan R 2006 Int. J. Mod. Phys. D 15 991
[34] Pun C S J, Kovács Z and Harko T 2008 Phys. Rev. D 78 024043
[35] Brandt C F C, Chan R, da Silva M F A and da Rocha J F V 2007 Gen. Rel. Grav. 39 1675
[36] Copeland E J, Sami M and Tsujikawa S 2006 Int. J. Mod. Phys. D 15 1753
[37] Padmanabhan T 2008 Gen. Rel. Grav. 40 529
[38] Hehl F W, Neeman Y, Nitsch J and Von der Heyde P 1978 Phys. Lett. B 78 102
[39] Hehl F W 1979 ''Four Lectures on Poincaré Gauge Theory'', in Proceedings of the 6th Course on Spin, Torsion and Supergravity, Eric, Italy, eds. Bergmann P G and de Sabbata V (New York: Plenum) p. 5
[40] Kawai T 1994 Phys. Rev. D 49 2862
[41] Kawai T 2000 Phys. Rev. D 62 104014
[42] Blagojević M and Vasilić M 2000 Class. Quantum Grav. 17 3785
[43] Blagojević M and Nikolić I A 2000 Phys. Rev. D 62 024021
[44] Hehl F W, MacCrea J D, Mielke E W and Ne'eman Y 1995 Phys. Rep. 258 1
[45] Hayashi K 1977 Phys. Lett. B 69 441
[46] Hayashi K and Shirafuji T 1979 Phys. Rev. D 19 3524
[47] Hayashi K and Shirafuji T 1981 Phys. Rev. D 24 3312
[48] Blagojević M and Vasilić M 1988 Class. Quantum Grav. 5 1241
[49] Kawai T, Shibata K and Tanaka I 2000 Prog. Theor. Phys. 104 505
[50] Nitsch J and Hehl F W 1980 Phys. Lett. B 90 98
[51] Leclerc M 2005 Phys. Rev. D 71 027503
[52] Mielke E W 2004 Phys. Rev. D 69 128501
[53] Mielke E W 1980 Phys. Rev. D 42 3388
[54] Obukhov Y N and Pereira J G 2004 Phys. Rev. D 69 128502
[55] Obukhov Y N and Pereira J G 2003 Phys. Rev. D 67 044016
[56] Meyer H 1982 Gen. Rel. Grav. 14 531
[57] Tung R S and Nester J M 1999 Phys. Rev. D 60 021501
[58] Ortín T 2004 Gravity and Strings (Cambridge: Cambridge University Press) p. 166
[59] Mφller C 1961 Ann. Phys. 12 118
[60] Mφller C 1961 Mat. Fys. Medd. Dan. Vid. Selsk. 1 10
[61] Mφller C 1964 Nucl. Phys. 57 330
[62] Mφller C 1978 Mat. Fys. Medd. Dan. Vid. Selsk. 39 13
[63] Pellegrini C and Plebański J 1963 Mat. Fys. Scr. Dan. Vid. Selsk. 2 No. 4
[64] Hehl F W 1980 Proceedings of the 6th School of Cosmology and Gravitation on Spin, Torsion, Rotation and Supergravity, Erice, Italy, eds. Bergmann P G and de Sabbata V (New York: Plenum)
[65] Hehl F W, McCrea J D, Mielke E W and Neeman Y 1995 Phys. Rep. 258 1
[66] Maluf J W, Faria F F and Castello-Branco K H 2003 Class. Quantum Grav. 20 4683
[67] Chang C C, Nester J M and Chen C M 1999 Phys. Rev. Lett. 83 1897
[68] Tung R S and Nester J M 1999 Phys. Rev. D 60 021501
[69] Nester J M and Yo Chin H J 1999 J. Phys. 37 113
[70] Nester J M, Ho F H and Chen C M 2003 ''Quasilocal Center-of-Mass for Teleparallel Gravity'', Proceeding of the 10th Marcel Grossman Meeting Rio de Janeiro, 2003 gr-qc/0403101
[71] Nester J M 1989 Phys. Lett. A 139 112
[72] Nester J M 1992 J. Math. Phys. 33 910
[73] Nester J M 1988 Class. Quantum Grav. 5 1003
[74] Maluf J W 1994 J. Math. Phys. 35 335
[75] Maluf J W and Kneip A 1997 J. Math. Phys. 38 458
[76] Maluf J W and da Rocha-Neto J F 1999 J. Math. Phys. 40 1490
[77] Maluf J W and Goya A 2001 Class. Quantum Grav. 18 5143
[78] Maluf J W, da Rocha-Neto J F, Toribio T M L and Castello-Branco K H 2002 Phys. Rev. D 65 124001
[79] Sousa A A and Maluf J W 2002 Prog. Theor. Phys. 108 457
[80] Szabados L B 2004 ''Quasi-Local Energy-Momentum and Angular Momentum in General Relativity'' (review article), Living Rev. Relativity 7 4http://www.livingreviews.org/lrr-2004-4
[81] de Andrade V C and Pereira J G 1997 Phys. Rev. D 56 4689
[82] de Andrade V C, Guillen L C T and Pereira J G 2000 Phys. Rev. Lett. 84 4533
[83] de Andrade V C, Guillen L C T and Pereira J G 2001 Phys. Rev. D 64 027502
[84] Nashed G G L 2008 Eur. Phys. J. C 54 291
[85] Nashed G G L 2007 Eur. Phys. J. C 51 377
[86] Nashed G G L 2007 Eur. Phys. J. C 49 851
[87] Maluf J W and Faria F F 2004 Ann. Phys. (Leipzig) 13 604
[88] Maluf J W, Ulhoa S C, Faria F F and da Rocha-Neto J F 2006 Calss. Quantum Grav. 23 6245
[89] Hirschmann E W, Wang A and Wu Y 2004 Class. Quantum Grav. 21 1791
[90] Elvang H, Emparan R, Mateos D and Reall H S 2004 Phys. Rev. Lett. 93 211302
[91] Hawking S W and Ellis G F R 1973 The Large Scale Structure of Spacetime (Cambridge: Cambridge University Press)
[92] Kawai T and Toma N 1990 Prog. Theor. Phys. 83 1
[93] Nashed G G L 2003 Chaos, Solitons and Fractals 15 841
[94] Tryon E P 1973 Nature 246 396
No Suggested Reading articles found!