Abstract
We consider the collision of two particles having distinct rest masses and orbiting near a Kerr-MOG black hole, and we further determine the center-of-mass energy (i.e., CME) associated with the particles. It is found that the CME energy is influenced not only by the rotation parameter a, but also by the MOG parameter \(\alpha\). Notably, it is shown that an extremal Kerr-MOG black hole case leads to surprisingly high the CME if and only if the parameter a satisfies the values given in the range \((0,\sqrt{1+\alpha })\) which diverges from that observed in Kerr-like black holes, thus highlighting the distinct characteristics of Kerr-MOG black holes. We present compelling evidence suggesting that Kerr-MOG black holes potentially act as significant generators for high-energy particles within the polar region.
Similar content being viewed by others
Data Availability
This research has no associated experimental and observational data.
References
J.W. Moffat, Scalar tensor vector gravity theory. JCAP 2006, 004 (2006) [arXiv:gr-qc/gr-qc/0506021]
J.W. Moffat, Time delay predictions in a modified gravity theory. Class. Quantum Gravit. 23, 6767–6771 (2006). arXiv:gr-qc/gr-qc/0605141
J.W. Moffat, V.T. Toth, Testing modified gravity with globular cluster velocity dispersions. ApJ 680, 1158–1161 (2008). https://doi.org/10.1086/587926. arXiv:astro-ph/0708.1935
J.W. Moffat, V.T. Toth, The bending of light and lensing in modified gravity. MNRAS 397, 1885–1892 (2009). https://doi.org/10.1111/j.1365-2966.2009.14876.x. arXiv:astro-ph/0805.4774
J.R. Brownstein, J.W. Moffat, The bullet cluster 1E0657-558 evidence shows modified gravity in the absence of dark matter. MNRAS 382, 29–47 (2007). https://doi.org/10.1111/j.1365-2966.2007.12275.x. arXiv:astro-ph/astro-ph/0702146
J.W. Moffat, A modified gravity and its consequences for the solar system, astrophysics and cosmology. Int. J. Mod. Phys. D 16, 2075–2090 (2007). https://doi.org/10.1142/S0218271807011577. arXiv:gr-qc/gr-qc/0608074
S. Rahvar, J.W. Moffat, Propagation of electromagnetic waves in MOG: gravitational lensing. MNRAS 482, 4514–4518 (2019). https://doi.org/10.1093/mnras/sty3002. arXiv:gr-qc/1807.07424
J. Moffat, S. Rahvar, V. Toth, Applying MOG to lensing: Einstein rings, Abell 520 and the bullet cluster. Galaxies 6, 43 (2018). https://doi.org/10.3390/galaxies6020043
A. Övgün, İ Sakallı, J. Saavedra, Weak gravitational lensing by Kerr-MOG black hole and Gauss-Bonnet theorem. Ann. Phys. 411, 167978 (2019). https://doi.org/10.1016/j.aop.2019.167978. arXiv:gr-qc/1806.06453
G.Y. Tuleganova, R.N. Izmailov, R.K. Karimov, A.A. Potapov, K.K. Nandi, Times of arrival (TOA) of signals in the Kerr-MOG black hole. Gen. Relativ. Gravit. 52, 31 (2020). https://doi.org/10.1007/s10714-020-02684-0
R.N. Izmailov, R.K. Karimov, E.R. Zhdanov, K.K. Nandi, Modified gravity black hole lensing observables in weak and strong field of gravity. MNRAS 483, 3754–3761 (2019). https://doi.org/10.1093/mnras/sty3350. arXiv:gr-qc/1905.01900
J.W. Moffat, Modified gravity black holes and their observable shadows. Eur. Phys. J. C 75, 130 (2015). https://doi.org/10.1140/epjc/s10052-015-3352-6. arXiv:gr-qc/1502.01677
J.W. Moffat, V.T. Toth, Masses and shadows of the black holes Sagittarius A* and M87* in modified gravity. Phys. Rev. D 101, 024014 (2020). https://doi.org/10.1103/PhysRevD.101.024014. arXiv:gr-qc/1904.04142
J.R. Mureika, J.W. Moffat, M. Faizal, Black hole thermodynamics in modified gravity (MOG). Phys. Lett. B 757, 528–536 (2016). https://doi.org/10.1016/j.physletb.2016.04.041. arXiv:gr-qc/1504.08226
L. Manfredi, J. Mureika, J. Moffat, Quasinormal modes of static modified gravity (MOG) black holes. In: proceedings of the journal of physics conference series, 2017, Vol. 942, Journal of Physics Conference Series, p. 012014. (2017). https://doi.org/10.1088/1742-6596/942/1/012014
L. Manfredi, J. Mureika, J. Moffat, Quasinormal modes of modified gravity (MOG) black holes. Phys. Lett. B 779, 492–497 (2018). https://doi.org/10.1016/j.physletb.2017.11.006. arXiv:gr-qc/1711.03199
L. Manfredi, J. Mureika, J. Moffat, Quasinormal modes of modified gravity (MOG) black holes. J. Undergrad. Rep. Phys. 29, 100006 (2019). https://doi.org/10.1063/1.5129246
M.A. Green, J.W. Moffat, V.T. Toth, Modified gravity (MOG), the speed of gravitational radiation and the event GW170817/GRB170817A. Phys. Lett. B 780, 300–302 (2018). https://doi.org/10.1016/j.physletb.2018.03.015. arXiv:gr-qc/1710.11177
K. Düztaş, Overspinning Kerr-MOG black holes by test fields and the third law of black hole dynamics. Eur. Phys. J. C 80, 19 (2020). https://doi.org/10.1140/epjc/s10052-020-7607-5. arXiv:gr-qc/1907.13435
M. Sharif, M. Shahzadi, Particle dynamics near Kerr-MOG black hole. Eur. Phys. J. C 77, 363 (2017). https://doi.org/10.1140/epjc/s10052-017-4898-2. arXiv:gr-qc/1705.03058
H.C. Lee, Y.J. Han, Innermost stable circular orbit of Kerr-MOG black hole. Eur. Phys. J. C 77, 655 (2017). https://doi.org/10.1140/epjc/s10052-017-5152-7. arXiv:gr-qc/1704.02740
D. Pérez, F.G.L. Armengol, G.E. Romero, Accretion disks around black holes in scalar-tensor-vector gravity. Phys. Rev. D 95, 104047 (2017). https://doi.org/10.1103/PhysRevD.95.104047. arXiv:astro-ph.HE/1705.02713
P. Pradhan, Study of energy extraction and epicyclic frequencies in Kerr-MOG (modified gravity) black hole. Eur. Phys. J. C 79, 401 (2019). https://doi.org/10.1140/epjc/s10052-019-6907-0. arXiv:gr-qc/1810.03290
M. Kološ, M. Shahzadi, Z. Stuchlík, Quasi-periodic oscillations around Kerr-MOG black holes. Eur. Phys. J. C 80, 133 (2020). https://doi.org/10.1140/epjc/s10052-020-7692-5
J. Rayimbaev, P. Tadjimuratov, A. Abdujabbarov, B. Ahmedov, M. Khudoyberdieva, Dynamics of test particles and twin peaks QPOs around regular black holes in modified gravity. Galaxies 9, 75 (2021). https://doi.org/10.3390/galaxies9040075. arXiv:gr-qc/2010.12863
R. Della Monica, I. de Martino, M. de Laurentis, Orbital precession of the S2 star in scalar-tensor-vector gravity. MNRAS 510, 4757–4766 (2022). https://doi.org/10.1093/mnras/stab3727. arXiv:gr-qc/2105.12687
R. Della Monica, I. de Martino, M. de Laurentis, Constraining modified gravity with the S2 star. Universe 8, 137 (2022). https://doi.org/10.3390/universe8020137. arXiv:gr-qc/2206.12699
B.V. Turimov, Comment on “orbital precession of the S2 star in scalar-tensor-vector gravity’’. MNRAS 516, 434–436 (2022). https://doi.org/10.1093/mnras/stac2113
R. Della Monica, I. de Martino, M. de Laurentis, Response to: comment on ‘orbital precession of the S2 star in scalar-tensor-vector gravity’. MNRAS 521, 474–477 (2023). https://doi.org/10.1093/mnras/stad579. arXiv:gr-qc/2302.12296
B. Turimov, H. Alibekov, P. Tadjimuratov, A. Abdujabbarov, Gravitational synchrotron radiation and Penrose process in STVG theory. Phys. Lett. B 843, 138040 (2023). https://doi.org/10.1016/j.physletb.2023.138040
M. Khodadi, D.F. Mota, A. Sheykhi, Harvesting energy driven by Comisso-Asenjo process from Kerr-MOG black holes. JCAP 2023, 034 (2023). https://doi.org/10.1088/1475-7516/2023/10/034. arXiv:astro-ph.HE/2307.00478
R.P. Fender, T.M. Belloni, E. Gallo, Towards a unified model for black hole X-ray binary jets. Mon. Not. R. Astron. Soc. 355, 1105–1118 (2004). https://doi.org/10.1111/j.1365-2966.2004.08384.x. arXiv:astro-ph/astro-ph/0409360
K. Auchettl, J. Guillochon, E. Ramirez-Ruiz, New physical insights about tidal disruption events from a comprehensive observational inventory at X-ray wavelengths. Astrophys. J. 838, 149 (2017). https://doi.org/10.3847/1538-4357/aa633b. arXiv:astro-ph.HE/1611.02291
The IceCube Collaboration.; et al.. Multimessenger observations of a flaring blazar coincident with high-energy neutrino IceCube-170922A. Science 2018, 361, eaat1378, [arXiv:gr-qc/1807.08816]. https://doi.org/10.1126/science.aat1378
M. Bañados, J. Silk, S.M. West, Kerr black holes as particle accelerators to arbitrarily high energy. Phys. Rev. Lett. 103, 111102 (2009). https://doi.org/10.1103/PhysRevLett.103.111102. arXiv:hep-ph/0909.0169
T. Jacobson, T.P. Sotiriou, Spinning black holes as particle accelerators. Phys. Rev. Lett. 104, 021101 (2010). https://doi.org/10.1103/PhysRevLett.104.021101. arXiv:gr-qc/0911.3363
K. Lake, Particle accelerators inside spinning black holes. Phys. Rev. Lett. 104, 211102 (2010). https://doi.org/10.1103/PhysRevLett.104.211102. arXiv:gr-qc/1001.5463
M. Kimura, K.I. Nakao, H. Tagoshi, Acceleration of colliding shells around a black hole: validity of the test particle approximation in the Banados-silk-west process. Phys. Rev. D 83, 044013 (2011). https://doi.org/10.1103/PhysRevD.83.044013. arXiv:gr-qc/1010.5438
O.B. Zaslavskii, Acceleration of particles as a universal property of rotating black holes. Phys. Rev. D 82, 083004 (2010). https://doi.org/10.1103/PhysRevD.82.083004. arXiv:gr-qc/1007.3678
O.B. Zaslavskii, Acceleration of particles by nonrotating charged black holes? Soviet J. Exp. Theor. Phys. Lett. 92, 571–574 (2010). https://doi.org/10.1134/S0021364010210010. arXiv:gr-qc/1007.4598
F. Atamurotov, B. Ahmedov, S. Shaymatov, Formation of black holes through BSW effect and black hole-black hole collisions. Astrophys. Space Sci. 347, 277–281 (2013). https://doi.org/10.1007/s10509-013-1527-x
O.B. Zaslavskii, Acceleration of particles by black holes: kinematic explanation. Phys. Rev. D 84, 024007 (2011). https://doi.org/10.1103/PhysRevD.84.024007. arXiv:gr-qc/1104.4802
S.R. Shaymatov, B.J. Ahmedov, A.A. Abdujabbarov, Particle acceleration near a rotating black hole in a Randall-Sundrum brane with a cosmological constant. Phys. Rev. D 88, 024016 (2013). https://doi.org/10.1103/PhysRevD.88.024016
O.B. Zaslavskii, Acceleration of particles by black holes–a general explanation. Class. Quantum Gravit. 28, 105010 (2011). https://doi.org/10.1088/0264-9381/28/10/105010. arXiv:gr-qc/1011.0167
A.A. Grib, Y.V. Pavlov, On particle collisions in the gravitational field of the Kerr black hole. Astropart. Phys. 34, 581–586 (2011). https://doi.org/10.1016/j.astropartphys.2010.12.005. arXiv:gr-qc/1001.0756
A.A. Grib, Y.V. Pavlov, On particle collisions near rotating black holes. Gravit. Cosmol. 17, 42–46 (2011). https://doi.org/10.1134/S0202289311010099. arXiv:gr-qc/1010.2052
M. Patil, P.S. Joshi, Naked singularities as particle accelerators. Phys. Rev. D 82, 104049 (2010). https://doi.org/10.1103/PhysRevD.82.104049. arXiv:gr-qc/1011.5550
M. Patil, P.S. Joshi, D. Malafarina, Naked singularities as particle accelerators. II. Phys. Rev. D 83, 064007 (2011). https://doi.org/10.1103/PhysRevD.83.064007. arXiv:gr-qc/1102.2030
M. Patil, P.S. Joshi, High energy particle collisions in superspinning Kerr geometry. Phys. Rev. D 84, 104001 (2011). https://doi.org/10.1103/PhysRevD.84.104001. arXiv:gr-qc/1103.1083
M. Patil, P. Joshi, Kerr naked singularities as particle accelerators. Class. Quantum Gravit. 28, 235012 (2011). https://doi.org/10.1088/0264-9381/28/23/235012. arXiv:gr-qc/1103.1082
T. Harada, M. Kimura, Collision of two general geodesic particles around a Kerr black hole. Phys. Rev. D 83, 084041 (2011). https://doi.org/10.1103/PhysRevD.83.084041. arXiv:gr-qc/1102.3316
S. Shaymatov, B. Ahmedov, Z. Stuchlík, A. Abdujabbarov, Effect of an external magnetic field on particle acceleration by a rotating black hole surrounded with quintessential energy. Int. J. Mod. Phys. D 27, 1850088 (2018). https://doi.org/10.1142/S0218271818500888
T. Harada, M. Kimura, Collision of an object in the transition from adiabatic inspiral to plunge around a Kerr black hole. Phys. Rev. D 84, 124032 (2011). https://doi.org/10.1103/PhysRevD.84.124032. arXiv:gr-qc/1109.6722
S. Shaymatov, D. Malafarina, B. Ahmedov, Effect of perfect fluid dark matter on particle motion around a static black hole immersed in an external magnetic field. Phys. Dark Universe 34, 100891 (2021). https://doi.org/10.1016/j.dark.2021.100891. arXiv:gr-qc/2004.06811
S. Shaymatov, B. Narzilloev, A. Abdujabbarov, C. Bambi, Charged particle motion around a magnetized Reissner-Nordström black hole. Phys. Rev. D 103, 124066 (2021). https://doi.org/10.1103/PhysRevD.103.124066. arXiv:gr-qc/2105.00342
A. Abdujabbarov, B. Ahmedov, B. Ahmedov, Energy extraction and particle acceleration around a rotating black hole in Hořava-Lifshitz gravity. Phys. Rev. D 84, 044044 (2011). https://doi.org/10.1103/PhysRevD.84.044044. arXiv:astro-ph.SR/1107.5389
P.J. Mao, R. Li, L.Y. Jia, J.R. Ren, Acceleration of particles in Einstein-Maxwell-dilaton black holes. Chin. Phys. C 41, 065101 (2017). https://doi.org/10.1088/1674-1137/41/6/065101. arXiv:hep-th/1008.2660
Y. Li, J. Yang, Y.L. Li, S.W. Wei, Y.X. Liu, Particle acceleration in Kerr-(anti-)de Sitter black hole backgrounds. Class. Quantum Gravit. 28, 225006 (2011). https://doi.org/10.1088/0264-9381/28/22/225006. arXiv:hep-th/1012.0748
M. Amir, S.G. Ghosh, Rotating Hayward’s regular black hole as particle accelerator. J. High Energy Phys. 2015, 15 (2015). https://doi.org/10.1007/JHEP07(2015)015. arXiv:gr-qc/1503.08553
M. Khurshudyan, N.S. Mazhari, D. Momeni, R. Myrzakulov, M. Raza, Observational constraints on models of the universe with time variable gravitational and cosmological constants along MOG. Int. J. Theor. Phys. 54, 484–505 (2015). https://doi.org/10.1007/s10773-014-2242-2. arXiv:gr-qc/1403.0081
J. Rayimbaev, P. Tadjimuratov, Can modified gravity silence radio-loud pulsars? Phys. Rev. D 102, 024019 (2020). https://doi.org/10.1103/PhysRevD.102.024019
J.W. Moffat, Black holes in modified gravity (MOG). Eur. Phys. J. C 75, 175 (2015). https://doi.org/10.1140/epjc/s10052-015-3405-x. arXiv:gr-qc/1412.5424
B. Turimov, S. Hayitov, Black holes as a collider of high energy particles. arXiv e-prints 2023, [arXiv:gr-qc/2307.01919]. https://doi.org/10.48550/arXiv.2307.01919
Acknowledgements
This research was supported by the Grants F-FA-2021-510 from the Uzbekistan Ministry for Innovative Development.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) 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
Turimov, B., Shaymatov, S. & Hayitov, S. Collisions of particles near Kerr-MOG black holes. Eur. Phys. J. Plus 138, 1022 (2023). https://doi.org/10.1140/epjp/s13360-023-04618-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-023-04618-6