# Rotating Hayward’s regular black hole as particle accelerator

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## Abstract

Recently, Bañados, Silk and West (BSW) demonstrated that the extremal Kerr black hole can act as a particle accelerator with arbitrarily high center-of-mass energy (*E*_{CM}) when the collision takes place near the horizon. The rotating Hayward’s regular black hole, apart from Mass (*M*) and angular momentum (*a*), has a new parameter *g* (*g >* 0 is a constant) that provides a deviation from the Kerr black hole. We demonstrate that for each *g*, with *M* = 1, there exist critical *a*_{ E } and *r* _{ H } ^{ E } , which corresponds to a regular extremal black hole with degenerate horizons, and *a*_{ E } decreases whereas *r* _{ H } ^{ E } increases with increase in *g*. While *a < a*_{ E } describe a regular non-extremal black hole with outer and inner horizons. We apply the BSW process to the rotating Hayward’s regular black hole, for different *g*, and demonstrate numerically that the *E*_{CM} diverges in the vicinity of the horizon for the extremal cases thereby suggesting that a rotating regular black hole can also act as a particle accelerator and thus in turn provide a suitable framework for Plank-scale physics. For a non-extremal case, there always exist a finite upper bound for the *E*_{CM}, which increases with the deviation parameter *g*.

## Keywords

Black Holes Classical Theories of Gravity Spacetime Singularities## Notes

### **Open Access**

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## References

- [1]M. Bañados, J. Silk and S.M. West,
*Kerr black holes as particle accelerators to arbitrarily high energy*,*Phys. Rev. Lett.***103**(2009) 111102 [arXiv:0909.0169] [INSPIRE].ADSCrossRefGoogle Scholar - [2]R.P. Kerr,
*Gravitational field of a spinning mass as an example of algebraically special metrics*,*Phys. Rev. Lett.***11**(1963) 237 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar - [3]E. Berti, V. Cardoso, L. Gualtieri, F. Pretorius and U. Sperhake,
*Comment on*‘*Kerr black holes as particle accelerators to arbitrarily high energy*’,*Phys. Rev. Lett.***103**(2009) 239001 [arXiv:0911.2243] [INSPIRE].ADSCrossRefGoogle Scholar - [4]M. Bañados, B. Hassanain, J. Silk and S.M. West,
*Emergent flux from particle collisions near a Kerr black hole*,*Phys. Rev.***D 83**(2011) 023004 [arXiv:1010.2724] [INSPIRE].ADSGoogle Scholar - [5]K.S. Thorne,
*Disk accretion onto a black hole. II. Evolution of the hole*,*Astrophys. J.***191**(1974) 507 [INSPIRE].ADSCrossRefGoogle Scholar - [6]T. Jacobson and T.P. Sotiriou,
*Spinning black holes as particle accelerators*,*Phys. Rev. Lett.***104**(2010) 021101 [arXiv:0911.3363] [INSPIRE].ADSCrossRefGoogle Scholar - [7]O.B. Zaslavskii,
*Acceleration of particles by nonrotating charged black holes*,*JETP Lett.***92**(2010) 571 [arXiv:1007.4598] [INSPIRE].ADSCrossRefGoogle Scholar - [8]S.-W. Wei, Y.-X. Liu, H.-T. Li and F.-W. Chen,
*Particle collisions on stringy black hole background*,*JHEP***12**(2010) 066 [arXiv:1007.4333] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [9]I. Hussain,
*Collision energy in the center-of-mass frame for rotating and accelerating black holes*,*Mod. Phys. Lett.***A 27**(2012) 1250017 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar - [10]T. Harada and M. Kimura,
*Black holes as particle accelerators: a brief review*,*Class. Quant. Grav.***31**(2014) 243001 [arXiv:1409.7502] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [11]K. Lake,
*Particle accelerators inside spinning black holes*,*Phys. Rev. Lett.***104**(2010) 211102 [arXiv:1001.5463] [INSPIRE].ADSCrossRefGoogle Scholar - [12]S.-W. Wei, Y.-X. Liu, H. Guo and C.-E. Fu,
*Charged spinning black holes as particle accelerators*,*Phys. Rev.***D 82**(2010) 103005 [arXiv:1006.1056] [INSPIRE].ADSGoogle Scholar - [13]C. Liu, S. Chen, C. Ding and J. Jing,
*Particle acceleration on the background of the Kerr-Taub-NUT spacetime*,*Phys. Lett.***B 701**(2011) 285 [arXiv:1012.5126] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [14]P.-J. Mao, L.-Y. Jia, J.-R. Ren and R. Li,
*Acceleration of particles in Einstein-Maxwell-dilaton black hole*, arXiv:1008.2660 [INSPIRE]. - [15]Y. Zhu, S.-F. Wu, Y.-X. Liu and Y. Jiang,
*General stationary charged black holes as charged particle accelerators*,*Phys. Rev.***D 84**(2011) 043006 [arXiv:1103.3848] [INSPIRE].ADSGoogle Scholar - [16]O.B. Zaslavskii,
*Acceleration of particles by black holes as a result of deceleration: ultimate manifestation of kinematic nature of BSW effect*,*Phys. Lett.***B 712**(2012) 161 [arXiv:1202.0565] [INSPIRE].ADSCrossRefGoogle Scholar - [17]O.B. Zaslavskii,
*Horizon bifurcation surface as particle accelerator*,*Int. J. Mod. Phys.***D 22**(2013) 1350044 [arXiv:1203.5291] [INSPIRE].ADSCrossRefGoogle Scholar - [18]O.B. Zaslavskii,
*Acceleration of particles by black holes: general explanation*,*Class. Quant. Grav.***28**(2011) 105010 [arXiv:1011.0167] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [19]A.A. Grib and Y.V. Pavlov,
*On particles collisions near rotating black holes*,*Grav. Cosmol.***17**(2011) 42 [arXiv:1010.2052] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [20]A.A. Grib, Y.V. Pavlov and O.F. Piattella,
*On collisions with unlimited energies in the vicinity of Kerr and Schwarzschild black hole horizons*,*Grav. Cosmol.***18**(2012) 70 [arXiv:1203.4952] [INSPIRE].ADSCrossRefMATHGoogle Scholar - [21]T. Harada and M. Kimura,
*Collision of two general geodesic particles around a Kerr black hole*,*Phys. Rev.***D 83**(2011) 084041 [arXiv:1102.3316] [INSPIRE].ADSGoogle Scholar - [22]C. Liu, S. Chen and J. Jing,
*Collision of two general geodesic particles around a Kerr-Newman black hole*,*Chin. Phys. Lett.***30**(2013) 100401 [arXiv:1104.3225] [INSPIRE].ADSCrossRefGoogle Scholar - [23]M. Patil and P.S. Joshi,
*Naked singularities as particle accelerators*,*Phys. Rev.***D 82**(2010) 104049 [arXiv:1011.5550] [INSPIRE].ADSGoogle Scholar - [24]M. Patil, P.S. Joshi and D. Malafarina,
*Naked singularities as particle accelerators. II*,*Phys. Rev.***D 83**(2011) 064007 [arXiv:1102.2030] [INSPIRE].ADSGoogle Scholar - [25]M. Patil and P.S. Joshi,
*Kerr naked singularities as particle accelerators*,*Class. Quant. Grav.***28**(2011) 235012 [arXiv:1103.1082] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar - [26]M. Patil, P.S. Joshi, M. Kimura and K.-i. Nakao,
*Acceleration of particles and shells by Reissner-Nordström naked singularities*,*Phys. Rev.***D 86**(2012) 084023 [arXiv:1108.0288] [INSPIRE].ADSGoogle Scholar - [27]P.S. Joshi,
*Gravitational collapse: the story so far*,*Pramana***55**(2000) 529 [gr-qc/0006101] [INSPIRE].ADSCrossRefGoogle Scholar - [28]S.A. Hayward,
*Formation and evaporation of regular black holes*,*Phys. Rev. Lett.***96**(2006) 031103 [gr-qc/0506126] [INSPIRE].ADSCrossRefGoogle Scholar - [29]J.M. Bardeen,
*Non-singular general-relativistic gravitational collapse*, in Proceedings of the*International Conference GR5*, Tiflis U.S.S.R. (1968).Google Scholar - [30]C. Bambi and L. Modesto,
*Rotating regular black holes*,*Phys. Lett.***B 721**(2013) 329 [arXiv:1302.6075] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar - [31]B. Toshmatov, B. Ahmedov, A. Abdujabbarov and Z. Stuchlik,
*Rotating regular black hole solution*,*Phys. Rev.***D 89**(2014) 104017 [arXiv:1404.6443] [INSPIRE].ADSMATHGoogle Scholar - [32]C. Bambi,
*Testing the Kerr black hole hypothesis*,*Mod. Phys. Lett.***A 26**(2011) 2453 [arXiv:1109.4256] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar - [33]C. Bambi,
*Testing the space-time geometry around black hole candidates with the available radio and X-ray data*,*Astron. Rev.***8**(2013) 4 [arXiv:1301.0361] [INSPIRE].ADSCrossRefGoogle Scholar - [34]S.G. Ghosh, P. Sheoran and M. Amir,
*Rotating Ayón-Beato-García black hole as a particle accelerator*,*Phys. Rev.***D 90**(2014) 103006 [arXiv:1410.5588] [INSPIRE].ADSGoogle Scholar - [35]
- [36]J.M. Bardeen, W.H. Press and S.A. Teukolsky,
*Rotating black holes: locally nonrotating frames, energy extraction and scalar synchrotron radiation*,*Astrophys. J.***178**(1972) 347 [INSPIRE].ADSCrossRefGoogle Scholar