Gödel-Type Universes in f(R) Gravity with an Arbitrary Coupling between Matter and Geometry
ZHANG Tao1, WU Pu-Xun2, YU Hong-Wei1,2**
1Department of Physics and Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081 2Center for Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211
Gödel-Type Universes in f(R) Gravity with an Arbitrary Coupling between Matter and Geometry
ZHANG Tao1, WU Pu-Xun2, YU Hong-Wei1,2**
1Department of Physics and Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081 2Center for Nonlinear Science and Department of Physics, Ningbo University, Ningbo 315211
摘要By studying the Gödel-type solution, the causality in f(R) gravity with an arbitrary coupling between matter and geometry is discussed. Assuming that the matter source is a perfect fluid and a scalar field, respectively, we find that for the perfect fluid case, noncausal Gödel−type solutions exist and there is a critical radius rc beyond which the causality is violated. For the scalar field case, the violation of causality is forbidden.
Abstract：By studying the Gödel-type solution, the causality in f(R) gravity with an arbitrary coupling between matter and geometry is discussed. Assuming that the matter source is a perfect fluid and a scalar field, respectively, we find that for the perfect fluid case, noncausal Gödel−type solutions exist and there is a critical radius rc beyond which the causality is violated. For the scalar field case, the violation of causality is forbidden.
ZHANG Tao;WU Pu-Xun;YU Hong-Wei;**
. Gödel-Type Universes in f(R) Gravity with an Arbitrary Coupling between Matter and Geometry[J]. 中国物理快报, 2011, 28(12): 120401-120401.
ZHANG Tao, WU Pu-Xun, YU Hong-Wei, **
. Gödel-Type Universes in f(R) Gravity with an Arbitrary Coupling between Matter and Geometry. Chin. Phys. Lett., 2011, 28(12): 120401-120401.
[1] Gödel K 1949 Rev. Mod. Phys. 21 447
[2] Som M M and Raychaudhuri A K 1968 Proc. R. Soc. London A 304 81
Reboucas M J 1979 Phys. Lett. A 70 161
Raychaudhuri A K and Guha Thakurta S N 1980 Phys. Rev. D 22 802
[3] Hiscock W A 1978 Phys. Rev. D 17 1497
Chakraborty S K and Bandyopadhyay N 1983 J. Math. Phys. 24 129
Panov V F 1991 Sov. Phys. J. 34 130
[4] Villalba V M 1993 Mod. Phys. Lett. A 8 3011
Pimentel L O, Camacho A and Macias A 1994 Mod. Phys. Lett. A 9 3703
Krechet V G and Sandina I V 1982 Sov. Phys. J. 24 950
Leahy D A 1982 Int. J. Theor. Phys. 21 703
Herrera A and Shikin G N 1996 Grav. Cosmol. 2 155
[5] Reboucas M J and Tiomno J 1983 Phys. Rev. D 28 1251
[6] Reboucas M J, Aman J E and Teixeira A F F 1986 J. Math. Phys. 27 1370
[7] Smalley L L 1985 Phys. Rev. D 32 3124
Duarte de Oliveira J, Teixeira A F F and Tiomno J 1986 Phys. Rev. D 34 3661
Accioly A J and Matsas G E A 1988 Phys. Rev. D 38 1083
[8] Reboucas M J and Santos J 2009 Phys. Rev. D 80 063009
[9] Clifton T and Barrow J D 2005 Phys. Rev. D 72 123003
[10] Santos J, Reboucas M J and Oliveira T B R F 2010 Phys. Rev. D 81 123017
[11] Nojiri S and Odintsov S D 2008 arXiv:0807.0685
Sotiriou T P and Faraoni V 2010 Rev. Mod. Phys. 82 451
De Felice A and Tsujikawa S 2010 Living Rev. Rel. 13 3
Nojiri S and Odintsov S D 2011 arXiv:1011.0544
[12] Nojiri S and Odintsov S D 2004 Phys. Lett. B 599 137
Allemandi G, Borowiec A, Francaviglia M and Odintsov S D 2005 Phys. Rev. D 72 063505
[13] Chiba T 2003 Phys. Lett. B 575 1
Amendola L and Tsujikawa S 2008 Phys. Lett. B 660 125
[14] Dicke R 2004 Gen. Rel. Grav. 36 217
Sotiriou T P 2006 Phys. Rev. D 73 063515
T P Sotiriou 2006 Gen. Rel. Grav. 38 1407
[15] Dolgov A D and Kawasaki M 2003 Phys. Lett. B 573 1
Faraoni V 2006 Phys. Rev. D 74 104071
Sotiriou T P 2007 Phys. Lett. B 645 389
[16] Frolov A V 2008 Phys. Rev. Lett. 101 061103
[17] Bertolami O, Boehmer C G, Harko T and Lobo F S N 2007 Phys. Rev. D 75 104016
[18] Bertolami O and Paramos J 2010 J. Cosmol. Astropart. Phys. 03 009
[19] Bertolami O, Frazao P and Paramos J 2010 Phys. Rev. D 81 104046
[20] Bertolami O, Lobo P S N and Paramos J 2008 Phys. Rev. D 78 064036
[21] Bertolami O, Frazao P and Paramos J 2011 Phys. Rev. D 83 044010
2011, Vol. 28 
