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Rotating charged black hole spacetimes in quadratic $f (R)$ $f (R)$ gravitational theories

G. G. L. Nashed

G. G. L. Nashed

Centre for Theoretical Physics, British University in Egypt, P.O. Box 43, 11837 Cairo, Egypt

Department of Mathematics, Faculty of Science, Ain Shams University, 11566 Cairo, Egypt

Egyptian Relativity Group (ERG), Cairo University, 12613 Giza, Egypt

E-mail Address: nashed@bue.edu.eg

E-mail Address: gglnashed@sci.asu.edu.eg

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https://doi.org/10.1142/S0218271818500748Cited by:54 (Source: Crossref)

Abstract

Motivated by the substantial modifications of gravitational theories and by the models that come out of $f (R)$ $f (R)$ , we apply the field equation of the charged $f (R) = R + β R^{2}$ $f (R) = R + β R^{2}$ as well as a general vector potential containing three unknown functions to two spherically symmetric spacetimes. We solve the output of the differential equations and derive a class of black holes that are electrically and magnetically rotating spacetimes. The asymptotic behavior of these black holes acts as anti-de Sitter spacetime. Moreover, these solutions have asymptotic curvature singularities as those of General Relativity. We investigate this by calculating the invariants of curvature. Also, we address the issue of the energy conditions and show that the strong energy condition is satisfied provided $β > 0$ $β > 0$ . Finally, we compute the conserved quantities like mass and angular momentum.

Keywords:

PACS: 04.50.Kd, 04.70.Bw, 04.20.Jb

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References

1. Supernova Search Team Collab. (A. G. Riess et al.), Astron. J. 116 (1998) 1009; Supernova Cosmology Project Collab. (S. Perlmutter et al.), Astrophys. J. 517 (1999) 565. Google Scholar
2. Planck Collab. (P. A. R. Ade et al.), Astron. Astrophys. 571 (2014) A16; D. N. Spergel et al., Astrophys. J. Suppl. 170 (2007) 377. Google Scholar
3. B. Jain and A. Taylor , Phys. Rev. Lett. 91 (2003) 141302. Crossref, Web of Science, ADS, Google Scholar
4. S. Cole et al., Mon. Not. R. Astron. Soc. 362 (2005) 505; D. J. Eisenstein et al.Astrophys. J. 633 (2005) 560; W. J. Percival et al., Mon. Not. R. Astron. Soc. 401 (2010) 2148; N. Padmanabhan et al., Mon. Not. R. Astron. Soc. 427 (2012) 2132; C. Blake et al., Mon. Not. R. Astron. Soc. 418 (2011) 1707; L. Anderson et al., Mon. Not. R. Astron. Soc. 428 (2013) 1036. Google Scholar
5. J. Simon, L. Verde and R. Jimenez, Phys. Rev. D 71 (2005) 123001; D. Stern, R. Jimenez, L. Verde, M. Kamionkowski and S. A. Stanford, J. Cosmol. Astropart. Phys. 1002 (2010) 008; C. Zhang, H. Zhang, S. Yuan, T. J. Zhang and Y. C. Sun, Res. Astron. Astrophys. 14 (2014) 1221; C. Blake et al., Mon. Not. R. Astron. Soc. 418 (2011) 1725; C. H. Chuang and Y. Wang, Mon. Not. R. Astron. Soc. 435 (2013) 255; M. Moresco et al., J. Cosmol. Astropart. Phys. 1208 (2012) 006. Google Scholar
6. E. Hawkins et al., Mon. Not. R. Astron. Soc. 346 (2003) 78; M. Tegmark et al., Phys. Rev. D 69 (2004) 103501. Google Scholar
7. R. Penrose, Phys. Rev. Lett. 14 (1965) 57; S. Hawking and R. Penrose, Proc. R. Soc. Lond. A 314 (1970) 529. Google Scholar
8. S. W. Hawking and G. F. R. Ellis , The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973). Crossref, Google Scholar
9. S. Weinberg , Rev. Mod. Phys. 61 (1989) 1. Crossref, Web of Science, ADS, Google Scholar
10. S. Nojiri and S. D. Odintsov, in Proc. 42nd Karpacz Winter School of Theoretical Physics Conf.: Current Mathematical Topics in Gravitation and Cosmology (2006); Int. J. Geom. Methods Mod. Phys. 4 (2007) 115; T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82 (2010) 451; T. Clifton, P. G. Ferreira, A. Padilla and C. Skordis, Phys. Rep. 513 (2012) 1. Google Scholar
11. A. De Felice and S. Tsujikawa , Living Rev. Rel. 13 (2010) 3. Crossref, Web of Science, ADS, Google Scholar
12. K. Koyama , Rep. Prog. Phys. 79 (2016) 046902. Crossref, Web of Science, Google Scholar
13. T. Harko, F. S. N. Lobo, S. Nojiri and S. D. Odintsov, Phys. Rev. D 84 (2011) 024020; K. Bamba, G. G. L. Nashed, W. El Hanafy and Sh. Kh. Ibraheem, Phys. Rev. D 94 (2016) 083513; M. Jamil, D. Momeni, M. Raza and R. Myrzakulov, Eur. Phys. J. C 72 (2012) 1999; G. G. L. Nashed, Chin. Phys. Lett. 29 (2012) 050402; F. G. Alvarenga, A. de la Cruz-Dombriz, M. J. S. Houndjo, M. E. Rodrigues and D. Saez-Gomez, Phys. Rev. D 87 (2013) 103526; Erratum 87 (2013) 129905. Google Scholar
14. K. Bamba, C.-Q. Geng, S. Nojiri and S. D. Odintsov, Europhys. Lett. 89 (2010) 50003; M. J. S. Houndjo, M. E. Rodrigues, D. Momeni and R. Myrzakulov, Can. J. Phys. 92 (2014) 1528; G. G. L. Nashed and W. El Hanafy, Eur. Phys. J. C 74 (2014) 3099; M. E. Rodrigues, M. J. S. Houndjo, D. Momeni and R. Myrzakulov, Can. J. Phys. 92 (2014) 173; A. Awad and G. G. L. Nashed, J. Cosmol. Astropart. Phys. 02 (2017) 046; K. Bamba, S. D. Odintsov, L. Sebastiani and S. Zerbini, Eur. Phys. J. C 67 (2010) 295; G. G. L. Nashed and W. El Hanafy, Eur. Phys. J. C 75 (2015) 279; S. Nojiri, S. D. Odintsov, A. Toporensky and P. Tretyakov, Gen. Relativ. Gravit. 42 (2010) 1997. Google Scholar
15. G. Cognola, E. Elizalde, S. Nojiri, S. D. Odintsov and S. Zerbini, Phys. Rev. D 73 (2006) 084007; E. Elizalde, R. Myrzakulov, V. V. Obukhov and D. Saez-Gomez, Class. Quantum Grav. 27 (2010) 095007; G. G. L. Nashed, Gen. Relativ. Gravit. 45 (2013) 1887; A. De Felice and T. Suyama, J. Cosmol. Astropart. Phys. 0906 (2009) 034; A. De Felice and S. Tsujikawa, Phys. Lett. B 675 (2009) 1; G. G. L. Nashed, Phys. Rev. D 88 (2013) 104034; S. Nojiri and S. D. Odintsov, Phys. Lett. B 631 (2005) 1; Phys. Rev. D 68 (2003) 123512; G. G. L. Nashed, Gen. Relativ. Gravit. 47(7) (2015) 75; G. G. L. Nashed, Eur. Phys. J. C 49(3) (2007) 851. Google Scholar
16. R. Aldrovandi and J. G. Pereira, An introduction to teleparallel gravity (2010), Classnotes, Instituto de Fisica Teorica, Sao Paulo, www.ift.unesp.br/users/jpereira/tele.pdf; R. Aldrovandi, J. G. Pereira and K. H. Vu, Braz. J. Phys. 34 (2004) 1374; J. W. Maluf, Ann. Phys. 525 (2013) 339. Google Scholar
17. R. Ferraro and F. Fiorini, Phys. Rev. D 75 (2007) 084031; T. Harko, F. S. N. Lobo, G. Otalora and E. N. Saridakis, Phys. Rev. D 89 (2014) 124036; S. Basilakos, S. Capozziello, M. De Laurentis, A. Paliathanasis and M. Tsamparlis, Phys. Rev. D 88 (2013) 103526; G. G. L. Nashed, Nuovo Cimento B 117 (2002) 521; K. Bamba, S. D. Odintsov and D. Sez-Gomez, Phys. Rev. D 88 (2013) 084042; G. G. L. Nashed, Int. J. Mod. Phys. D 24 (2015) 1550007; M. E. Rodrigues, M. J. S. Houndjo, D. Saez-Gomez and F. Rahaman, Phys. Rev. D 86 (2012) 104059; C. Xu, E. N. Saridakis and G. Leon, J. Cosmol. Astropart. Phys. 1207 (2012) 005; C. G. Bohmer, T. Harko and F. S. N. Lobo, Phys. Rev. D 85 (2012) 044033; A. Awad, S. Capozziello and G. G. L. Nashed, J. Cosmol. Astropart. Phys. 7 (2017) 136; J. B. Dent, S. Dutta and E. N. Saridakis, J. Cosmol. Astropart. Phys. 1101 (2011) 009; B. Li, T. P. Sotiriou and J. D. Barrow, Phys. Rev. D 83 (2011) 064035. Google Scholar
18. F. Kiani and K. Nozari, Phys. Lett. B 728 (2014) 554; T. Harko, F. S. N. Lobo, G. Otalora and E. N. Saridakis, J. Cosmol. Astropart. Phys. 12 (2014) 021. Google Scholar
19. G. Kofinas and E. N. Saridakis , Phys. Rev. D 90 (2014) 084044. Crossref, Web of Science, ADS, Google Scholar
20. A. de la Cruz-Dombriz, P. K. S. Dunsby, V. C. Busti and S. Kandhai , Phys. Rev. D 89 (2014) 064029. Crossref, Web of Science, ADS, Google Scholar
21. A. de la Cruz-Dombriz, A. Dobado and A. L. Maroto , Phys. Rev. D 80 (2009) 124011. Crossref, Web of Science, ADS, Google Scholar
22. J. A. R. Cembranos, A. de la Cruz-Dombriz and P. Jimeno Romero , Int. J. Geom. Methods Mod. Phys. 11 (2014) 1450001. Link, Web of Science, Google Scholar
23. A. A. Starobinsky , Phys. Lett. B 91 (1980) 99. Crossref, Web of Science, ADS, Google Scholar
24. A. A. Starobinsky , Sov. Astron. Lett. 9 (1983) 302. Web of Science, ADS, Google Scholar
25. A. V. Astashenok, A. de la Cruz-Dombriz and S. D. Odintsov , Class. Quantum Grav. 34 (2017) 205008. Crossref, Web of Science, ADS, Google Scholar
26. A. A. Starobinsky , JETP Lett. 86 (2007) 157. Crossref, Web of Science, ADS, Google Scholar
27. W. Hu and I. Sawicki , Phys. Rev. D 76 (2007) 064004. Crossref, Web of Science, ADS, Google Scholar
28. S. A. Appleby and R. A. Battye , Phys. Lett. B 654 (2007) 7. Crossref, Web of Science, ADS, Google Scholar
29. A. de la Cruz-Dombriz, P. K. S. Dunsby, O. Luongo and L. Reverberi , J. Cosmol. Astropart. Phys. 1612 (2016) 042. Crossref, Web of Science, ADS, Google Scholar
30. A. de la Cruz-Dombriz, E. Elizalde, S. D. Odintsov and D. Saez-Gomez , J. Cosmol. Astropart. Phys. 05 (2016) 060. Crossref, Web of Science, ADS, Google Scholar
31. M. Born and L. Infeld , Proc. R. Soc. Lond. A 144 (1934) 425. Crossref, ADS, Google Scholar
32. A. Peres , Phys. Rev. 122 (1961) 273. Crossref, Web of Science, ADS, Google Scholar
33. L. Balart, Mod. Phys. Lett. A 24 (2009) 2777; E. Ayon-Beato and A. Garcia, Phys. Lett. B 464 (1999) 25; Phys. Rev. Lett. 80 (1998) 5056; K. A. Bronnikov, Phys. Rev. D 63 (2001) 044005; I. Dymnikova, Class. Quantum Grav. 21 (2004) 4417; A. Garcia, E. Hackmann, C. Lammerzahl and A. Macias, Phys. Rev. D 86 (2012) 024037; G. W. Gibbons and D. A. Rasheed, Phys. Lett. B 365 (1996) 46; F. S. N. Lobo and A. V. B. Arellano, Class. Quantum Grav. 24 (2007) 1069; G. J. Olmo and D. Rubiera-Garcia, Phys. Rev. D 84 (2011) 124059; L. Balart and E. C. Vagenas, Phys. Rev. D 90 (2014) 124045; J. A. R. Cembranos, A. de la Cruz-Dombriz and J. Jarillo, J. Cosmol. Astropart. Phys. 02 (2015) 042. Google Scholar
34. J. M. Bardeen , in Proc. Int. Conf. GR5 (1968). Google Scholar
35. M. E. Rodrigues, J. C. Fabris, E. L. B. Junior and G. T. Marques , Eur. Phys. J. C 76 (2016) 250. Crossref, Web of Science, ADS, Google Scholar
36. E. Ayon-Beato and A. Garcia, Phys. Lett. B 493 (2000) 149; E. Ayon-Beato and A. Garcia, Phys. Rev. Lett. 80 (1998) 5056; K. A. Bronnikov, Phys. Rev. Lett. 85 (2000) 4641. Google Scholar
37. I. G. Dymnikova, Gen. Relativ. Gravit. 24 (1992) 235; Phys. Lett. B 472 (2000) 33; Int. J. Mod. Phys D. 12 (2003) 1015; K. A. Bronnikov and I. Dymnikova, Class. Quantum Grav. 24 (2007) 5803; M. Azreg-Ainou, G. Clement, J. C. Fabris and M. E. Rodrigues, Phys. Rev. D 83 (2011) 124001; K. A. Bronnikov and J. C. Fabris, Phys. Rev. Lett. 96 (2006) 251101; J. P. S. Lemos and V. T. Zanchin, Phys. Rev. D 83 (2011) 124005. Google Scholar
38. F. Briscese, E. Elizalde, S. Nojiri and S. D. Odintsov , Phys. Lett. B 646 (2007) 105. Crossref, Web of Science, ADS, Google Scholar
39. K. Bamba, S. Nojiri and S. D. Odintsov , J. Cosmol. Astropart. Phys. 0810 (2008) 045. Crossref, Web of Science, ADS, Google Scholar
40. E. Babichev and D. Langlois , Phys. Rev. D 81 (2010) 124051. Crossref, Web of Science, ADS, Google Scholar
41. A. Awad, S. Capozziello and G. G. L. Nashed , J. High Energy Phys. 2017 (2017) 136. Crossref, Web of Science, Google Scholar
42. M. Hassaine and C. Martinez , Phys. Rev. D 75 (2007) 027502. Crossref, Web of Science, ADS, Google Scholar
43. G. Cognola, E. Elizalde, S. Nojiri, S. D. Odintsov and S. Zerbini , J. Cosmol. Astropart. Phys. 0502 (2005) 010. Crossref, Web of Science, ADS, Google Scholar
44. T. Koivisto and H. Kurki-Suonio , Class. Quantum Grav. 23 (2006) 2355. Crossref, Web of Science, ADS, Google Scholar
45. A. Sheykhi , Phys. Rev. D 86 (2012) 024013. Crossref, Web of Science, ADS, Google Scholar
46. S. Capozziello , Int. J. Mod. Phys. D 11 (2002) 483. Link, Web of Science, ADS, Google Scholar
47. A. M. Awad , Class. Quantum Grav. 20 (2003) 2827. Crossref, Web of Science, ADS, Google Scholar
48. S. Carroll , Spacetime and Geometry: An Introduction to General Relativity, Addison-Wesley, Reading, (2004). Google Scholar
49. F. D. Albareti, J. A. R. Cembranos, A. de la Cruz-Dombriz and A. Dobado , J. Cosmol. Astropart. Phys. 1307 (2013) 009. Crossref, Web of Science, ADS, Google Scholar
50. A. Komar , Phys. Rev. 127 (1962) 1411. Crossref, Web of Science, ADS, Google Scholar
51. T. Shirafuji, G. G. L. Nashed and Y. Kobayashi , Prog. Theor. Phys. 96 (1996) 933. Crossref, Web of Science, ADS, Google Scholar
52. A. Komar , Phys. Rev. 113 (1959) 934. Crossref, Web of Science, ADS, Google Scholar
53. J. Winicour , in General Relativity and Gravitation, ed. A. Held (Plenum Press, New York, 1980). Google Scholar
54. A. Ashtekar , in Cosmology and Gravitation, eds. P. G. Bergmann and V. de Sabbata (Plenum Press, New York, 1980). Google Scholar
55. Y. Obukhov and G. F. Rubilar , Phys. Rev. D 74 (2006) 064002. Crossref, Web of Science, ADS, Google Scholar
56. T. Moon, Y. S. Myung and E. J. Son , Gen Relativ. Gravit. 43 (2011) 3079. Crossref, Web of Science, ADS, Google Scholar