Abstract
A charged rotating black hole in f(R) gravity is characterized by mass, M, spin, a, electric charge, Q, and \(R_{0}\) which is proportional to cosmological constant. We analyze the image of the black hole shadow in four types (1) at \(r\rightarrow \infty \), (2) at \(r\rightarrow r_{O}\) in vacuum, (3) at \(r\rightarrow \infty \) and (4) at \(r\rightarrow r_{O}\) for an observer at the presence of plasma. Moreover, we investigate the effect of spin, charge, and modification of gravity on the shape of the shadow. In addition, we use two observable parameters, the radius \(R_{s}\) and the distortion parameter \(\delta _{s}\), characterizing the apparent shape. We show that the shadow becomes smaller with increasing electric charge for all cases. Also, by increasing the rotation parameters, the circular symmetry of the black hole’s shadow image will change. Furthermore, in the presence of plasma, the plasma parameter also affects the size of the shadow.
Similar content being viewed by others
Data availability
No data associated in the manuscript.
References
T.D. Abbott et al., LIGO scientific and virgo collaborations. Phys. Rev. X 6, 041014 (2016)
B.P. Abbott et al., LIGO scientific and virgo collaborations. Phys. Rev. Lett. 116, 061102 (2016)
Event Horizon Telescope. Collaboration et al., Astrophys. J. 875, L1 (2019)
Event Horizon Telescope. Collaboration et al., Astrophys. J. 875, L2 (2019)
Event Horizon Telescope. Collaboration et al., Astrophys. J. 875, L3 (2019)
Event Horizon Telescope. Collaboration et al., Astrophys. J. 875, L4 (2019)
Event Horizon Telescope. Collaboration et al., Astrophys. J. 875, L5 (2019)
Event Horizon Telescope. Collaboration et al., Astrophys. J. 875, L6 (2019)
S.S. Doeleman et al., Science 338, 355 (2012)
K. Akiyama et al., Astrophys. J. 807, 150 (2015)
M. Wang, S. Chen, J. Wang, and J. Jing, arXiv:1904.12423 [gr-qc]
P.V. Cunha, C.A.R. Herdeiro, B. Kleihaus, J. Kunz, E. Radu, Phys. Lett. B 768, 373 (2017)
M. Wang, S. Chen, J. Jing, J. Cosmol. Astropart. Phys. 10, 051 (2017)
Z. Younsi, A. Zhidenko, L. Rezzolla, R. Konoplya, Y. Mizuno, Phys. Rev. D 94, 084025 (2016)
M. Amir, B.P. Singh, S.G. Ghosh, Eur. Phys. J. C 78, 399 (2018)
S.W. Wei, Y.X. Liu, J. Cosmol. Astropart. Phys. 2013, 063 (2013)
J. M. Bardeen, Gordon and Breach. in Black Holes (Les Astres Occlus), C. DeWitt and B. S. DeWitt (eds.). p 215 ,New York (1973)
A. de Vries Class. Quant. Grav. 17, 123 (2000)
A. Abdujabbarov, F. Atamurotov, Y. Kucukakca, B. Ahmedov, U. Camci, Astrophys. Space Sci. 344, 429 (2013)
A.A. Abdujabbarov, L. Rezzolla, B.J. Ahmedov, Mon. Not. Roy. Astron. Soc. 454, 2423 (2015)
A. Ovgun, I. Sakalli, J. Saavedra, J. Cosmol. Astropart. Phys. 10, 041 (2018)
S. Haroon, M. Jamil, K. Jusufi, K. Lin, R.B. Mann, Phys. Rev. D 99, 044015 (2019)
Z. Stuchlik, D. Charbulak, J. Schee, Eur. Phys. J. C 78, 180 (2018)
J.W. Mofft, Eur. Phys. J. C 75, 175 (2015)
H.M. Wang, Y.M. Xu, S.W. Wei, J. Cosmol. Astropart. Phys. 2019, 046 (2019)
Z. Li, C. Bambi, JCAP 1401, 041 (2014)
A. Abdujabbarov, M. Amir, B. Ahmedov, S.G. Ghosh, Phys. Rev. D 93, 104004 (2016)
A. Yumoto, D. Nitta, T. Chiba, N. Sugiyama, Phys. Rev. D 86, 103001 (2012)
L. Amarilla, E.F. Eiroa, G. Giribet, Phys. Rev. D 81, 124045 (2010)
L. Amarilla, E.F. Eiroa, Phys. Rev. D 85, 064019 (2012)
P.V.P. Cunha, C.A.R. Herdeiro, E. Radu, H.F. Runarsson, Phys. Rev. Lett. 115(21), 211102 (2015)
F.H. Vincent, E. Gourgoulhon, C. Herdeiro, E. Radu, Phys. Rev. D 94(8), 084045 (2016)
S. Dastan, R. Saffari and S. Soroushfar, arXiv:1610.09477 [gr-qc]
M. Sharif, S. Iftikhar, Eur. Phys. J. C 76, 630 (2016)
C. Bambi, N. Yoshida, Class. Quant. Grav. 27, 205006 (2010)
K. Jusufi, M. Jamil, P. Salucci, T. Zhu, and S. Haroon, arXiv:1905.11803 [physics.gen-ph]
X. Hou, Z. Xu, M. Zhou, J. Wang, J. Cosmol. Astropart. Phys. 2018, 015 (2018)
R. A. Konoplya, arXiv: 1905.00064 [gr-qc]
S. Haroon, K. Jusufi and M. Jamil, arXiv:1904.00711 [gr-qc]
C. Bambi, K. Freese, S. Vagnozzi and L. Visinelli, arXiv:1904.12983 [gr-qc]
S. Vagnozzi and L. Visinelli, arXiv:1905.12421 [gr-qc]
R. Shaikh, P. Kocherlakota, R. Narayan, P.S. Joshi, Mon. Not. Roy. Astron. Soc. 482, 52 (2019)
C. Bambi, K. Freese, Phys. Rev. D 79, 043002 (2009)
S.W. Wei, Y.X. Liu, R.B. Mann, Phys. Rev. D 99, 041303 (2019)
S. W. Wei, Y. C. Zou, Y. X. Liu, and R. B. Mann, arXiv:1904.07710 [gr-qc]
T. Zhu, Q. Wu, M. Jamil, K. Jusufi, arXiv:1906.05673
K. Jusufi, M. Jamil, P. Salucci, T. Zhu, S. Haroon, arXiv:1905.11803
P. Brax, C. van de Bruck, Class. Quant. Grav. 20, R201 (2003)
D. Lovelock, J. Math. Phys. 12, 498 (1971)
C. Brans, R.H. Dicke, Phys. Rev. 124, 925 (1961)
Y. Fujii, K. Maeda, The scalar-tensor theory of gravitation (Cambridge University Press, Cambridge, 2003)
S. Soroushfar, R. Saffari, J. Kunz, C. Lämmerzahl, Phys. Rev. D 92(4), 044010 (2015)
S. Soroushfar, R. Saffari, N. Kamvar, Eur. Phys. J. C 76(9), 476 (2016)
A.G. Riess et al., Supernova search team collaboration. Astron. J. 116, 1009 (1998)
S. Perlmutter et al., Supernova Cosmology Project Collaboration. Astrophys. J. 517, 565 (1999)
J.L. Tonry et al., Supernova search team collaboration. Astrophys. J. 594, 1 (2003)
C.L. Bennett et al., WMAP collaboration. Astrophys. J. Suppl. 148, 1 (2003)
G. Hinshaw et al., WMAP collaboration. Astrophys. J. Suppl. 170, 288 (2007)
H.A. Buchdahl, Mon. Not. Roy. Astron. Soc. 150, 1 (1970)
A.A. Starobinsky, Phys. Lett. B 91, 99 (1980)
K. Bamba, S.D. Odintsov, JCAP 0804, 024 (2008)
M. Akbar, R.G. Cai, Phys. Lett. B 648, 243 (2007)
G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov, L. Sebastiani, S. Zerbini, Phys. Rev. D 77, 046009 (2008)
C. Corda, Int. J. Mod. Phys. D 18, 2275 (2009)
S. Capozziello, F. Darabi, D. Vernieri, Mod. Phys. Lett. A 25, 3279 (2010)
S.H. Hendi, D. Momeni, Eur. Phys. J. C 71, 1823 (2011)
S. Asgari, R. Saffari, Gen. Rel. Grav. 44, 737 (2012)
S.H. Mazharimousavi, M. Halilsoy, T. Tahamtan, Eur. Phys. J. C 72, 1958 (2012)
S.G. Ghosh, S.D. Maharaj, U. Papnoi, Eur. Phys. J. C 73, 2473 (2013)
S. H. Hendi, B. Eslam Panah and R. Saffari, Int. J. Mod. Phys. D 23, 1450088 (2014)
R. Saffari, S. Rahvar, Phys. Rev. D 77, 104028 (2008)
S. Chakraborty, S. SenGupta, Eur. Phys. J. C 75, 11 (2015)
S. Chakraborty, S. SenGupta, Eur. Phys. J. C 75, 538 (2015)
V. Faraoni and T. P. Sotiriou, arXiv:1303.0746 [gr-qc]
J.L. Synge, Mon. Not. Roy. Astron. Soc. 131, 463 (1966)
S. Chandrasekhar, The mathematical theory of black holes (CLARENDON, OXFORD, UK, 1985)
K. Hioki and K. i. Maeda, Phys. Rev. D 80, 024042 (2009)
A. Grenzebach, V. Perlick, C. Lämmerzahl, Phys. Rev. D 89(12), 124004 (2014)
A. Larranaga, J. Phys. 78, 697 (2012)
B. Carter, Phys. Rev. 174, 5 (1968)
S.W. Wei, Y.X. Liu, JCAP 1311, 063 (2013)
J.M. Bardeen, W.H. Press, S.A. Teukolsky, Astrophys. J. 178, 347 (1972)
S.E. Vazquez, E.P. Esteban, Nuovo Cim. B 119, 489 (2004)
R. Takahashi, Publ. Astron. Soc. Jap. 57, 273 (2005)
A.A. Abdujabbarov, L. Rezzolla, B.J. Ahmedov, Mon. Not. Roy. Astron. Soc. 454, 2423 (2015)
J.B. Griffiths, J. Podolski, Exact space-times in Einstein’s general relativity (Cambridge University Press, Cambridge, 2009)
J. Bicak, P. Hadrava, Res. Astron. Astrophys. 44, 389 (1975)
O.Y. Tsupko, G.S. Bisnovatyi-Kogan, Grav. Cosmol. 18, 117 (2012)
V.S. Morozova, B.J. Ahmedov, A.A. Tursunov, Astrophys. Space Sci. 346, 513 (2013)
X. Er, S. Mao, Mon. Not. Roy. Astron. Soc. 437, 2180 (2014)
J.L. Synge, Relativity: the general theory (Interscience Publishers, New York, 1960)
F. Atamurotov, B. Ahmedov and A. Abdujabbarov Phys. Rev. D 92, 084005 (2015)
G.S. Bisnovatyi-Kogan, O.Y. Tsupko, Mon. Not. Roy. Astron. Soc. 404, 1790 (2010)
A. Abdujabbarov, B. Toshmatov, Z. Stuchlík, B. Ahmedov, Int. J. Mod. Phys. D 26, 1750051 (2016)
A. Rogers, Mon. Not. Roy. Astron. Soc. 451, 17 (2015)
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Dastan, S., Saffari, R. & Soroushfar, S. Shadow of a charged rotating black hole in f(R) gravity. Eur. Phys. J. Plus 137, 1002 (2022). https://doi.org/10.1140/epjp/s13360-022-03218-0
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-022-03218-0