Abstract
We have investigated the upper bound of the radiation energy in the head-on collision of two Myers-Perry black holes. Initially, the two black holes are far away from each other, and they become one black hole after the collision. We have obtained the upper bound of the radiation energy thermodynamically allowed in the process. The upper bound of the radiation energy is obtained in general dimensions. The radiation bound depends on the alignments of rotating axes for a given initial condition due to spin-spin interaction. We have found that the collision may not be occurred for a initially ultra-spinning black hole.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Virgo and LIGO Scientific collaborations, B.P. Abbott et al., Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116 (2016) 061102 [arXiv:1602.03837] [INSPIRE].
ATLAS collaboration, Combined search for the Standard Model Higgs boson using up to 4.9 fb −1 of pp collision data at \( \sqrt{s}=7 \) TeV with the ATLAS detector at the LHC, Phys. Lett. B 710 (2012) 49 [arXiv:1202.1408] [INSPIRE].
CMS collaboration, Combined results of searches for the standard model Higgs boson in pp collisions at \( \sqrt{s}=7 \) TeV, Phys. Lett. B 710 (2012) 26 [arXiv:1202.1488] [INSPIRE].
S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. D 16 (1977) 1248] [INSPIRE].
C.G. Callan Jr. and S.R. Coleman, The Fate of the False Vacuum. 2. First Quantum Corrections, Phys. Rev. D 16 (1977) 1762 [INSPIRE].
S.R. Coleman and F. De Luccia, Gravitational Effects on and of Vacuum Decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].
P. Burda, R. Gregory and I. Moss, Gravity and the stability of the Higgs vacuum, Phys. Rev. Lett. 115 (2015) 071303 [arXiv:1501.04937] [INSPIRE].
P. Burda, R. Gregory and I. Moss, Vacuum metastability with black holes, JHEP 08 (2015) 114 [arXiv:1503.07331] [INSPIRE].
R. Penrose, Gravitational collapse: The role of general relativity, Riv. Nuovo Cim. 1 (1969) 252 [Gen. Rel. Grav. 34 (2002) 1141] [INSPIRE].
R.M. Wald, Gedanken experiments to destroy a black hole, Annals Phys. 82 (1974) 548.
T. Jacobson and T.P. Sotiriou, Over-spinning a black hole with a test body, Phys. Rev. Lett. 103 (2009) 141101 [Erratum ibid. 103 (2009) 209903] [arXiv:0907.4146] [INSPIRE].
E. Barausse, V. Cardoso and G. Khanna, Test bodies and naked singularities: Is the self-force the cosmic censor?, Phys. Rev. Lett. 105 (2010) 261102 [arXiv:1008.5159] [INSPIRE].
E. Barausse, V. Cardoso and G. Khanna, Testing the Cosmic Censorship Conjecture with point particles: the effect of radiation reaction and the self-force, Phys. Rev. D 84 (2011) 104006 [arXiv:1106.1692] [INSPIRE].
M. Colleoni and L. Barack, Overspinning a Kerr black hole: the effect of self-force, Phys. Rev. D 91 (2015) 104024 [arXiv:1501.07330] [INSPIRE].
M. Colleoni, L. Barack, A.G. Shah and M. van de Meent, Self-force as a cosmic censor in the Kerr overspinning problem, Phys. Rev. D 92 (2015) 084044 [arXiv:1508.04031] [INSPIRE].
V. Cardoso and L. Queimada, Cosmic Censorship and parametrized spinning black-hole geometries, Gen. Rel. Grav. 47 (2015) 150 [arXiv:1511.00690] [INSPIRE].
V.E. Hubeny, Overcharging a black hole and cosmic censorship, Phys. Rev. D 59 (1999) 064013 [gr-qc/9808043] [INSPIRE].
S. Isoyama, N. Sago and T. Tanaka, Cosmic censorship in overcharging a Reissner-Nordström black hole via charged particle absorption, Phys. Rev. D 84 (2011) 124024 [arXiv:1108.6207] [INSPIRE].
R.C. Myers and M.J. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys. 172 (1986) 304 [INSPIRE].
M. Bouhmadi-Lopez, V. Cardoso, A. Nerozzi and J.V. Rocha, Black holes die hard: can one spin-up a black hole past extremality?, Phys. Rev. D 81 (2010) 084051 [arXiv:1003.4295] [INSPIRE].
J. Doukas, Exact constraints on D ≤ 10 Myers Perry black holes and the Wald Problem, Phys. Rev. D 84 (2011) 064046 [arXiv:1009.6118] [INSPIRE].
A. Saa and R. Santarelli, Destroying a near-extremal Kerr-Newman black hole, Phys. Rev. D 84 (2011) 027501 [arXiv:1105.3950] [INSPIRE].
S. Gao and Y. Zhang, Destroying extremal Kerr-Newman black holes with test particles, Phys. Rev. D 87 (2013) 044028 [arXiv:1211.2631] [INSPIRE].
J.V. Rocha, R. Santarelli and T. Delsate, Collapsing rotating shells in Myers-Perry-AdS 5 spacetime: A perturbative approach, Phys. Rev. D 89 (2014) 104006 [arXiv:1402.4161] [INSPIRE].
J.V. Rocha and R. Santarelli, Flowing along the edge: spinning up black holes in AdS spacetimes with test particles, Phys. Rev. D 89 (2014) 064065 [arXiv:1402.4840] [INSPIRE].
B. McInnes and Y.C. Ong, A Note on Physical Mass and the Thermodynamics of AdS-Kerr Black Holes, JCAP 11 (2015) 004 [arXiv:1506.01248] [INSPIRE].
J.V. Rocha and V. Cardoso, Gravitational perturbation of the BTZ black hole induced by test particles and weak cosmic censorship in AdS spacetime, Phys. Rev. D 83 (2011) 104037 [arXiv:1102.4352] [INSPIRE].
B. Gwak and B.-H. Lee, Cosmic Censorship of Rotating Anti-de Sitter Black Hole, JCAP 02 (2016) 015 [arXiv:1509.06691] [INSPIRE].
B. Gwak and B.-H. Lee, Thermodynamics of Three-dimensional Black Holes via Charged Particle Absorption, Phys. Lett. B 755 (2016) 324 [arXiv:1510.08215] [INSPIRE].
J. Natario, L. Queimada and R. Vicente, Test fields cannot destroy extremal black holes, arXiv:1601.06809 [INSPIRE].
L. Lehner and F. Pretorius, Black Strings, Low Viscosity Fluids and Violation of Cosmic Censorship, Phys. Rev. Lett. 105 (2010) 101102 [arXiv:1006.5960] [INSPIRE].
P. Figueras, M. Kunesch and S. Tunyasuvunakool, End Point of Black Ring Instabilities and the Weak Cosmic Censorship Conjecture, Phys. Rev. Lett. 116 (2016) 071102 [arXiv:1512.04532] [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
S.W. Hawking, Black Holes and Thermodynamics, Phys. Rev. D 13 (1976) 191 [INSPIRE].
J.M. Bardeen, Kerr Metric Black Holes, Nature 226 (1970) 64 [INSPIRE].
R. Penrose and R.M. Floyd, Extraction of rotational energy from a black hole, Nature 229 (1971) 177 [INSPIRE].
D. Christodoulou, Reversible and irreversible transforations in black hole physics, Phys. Rev. Lett. 25 (1970) 1596 [INSPIRE].
D. Christodoulou and R. Ruffini, Reversible transformations of a charged black hole, Phys. Rev. D 4 (1971) 3552 [INSPIRE].
L. Smarr, Mass formula for Kerr black holes, Phys. Rev. Lett. 30 (1973) 71 [Erratum ibid. 30 (1973) 521] [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
J.D. Bekenstein, Generalized second law of thermodynamics in black hole physics, Phys. Rev. D 9 (1974) 3292 [INSPIRE].
B. Gwak and B.-H. Lee, Rotating Black Hole Thermodynamics with a Particle Probe, Phys. Rev. D 84 (2011) 084049 [arXiv:1106.1483] [INSPIRE].
M. Shibata and H. Yoshino, Nonaxisymmetric instability of rapidly rotating black hole in five dimensions, Phys. Rev. D 81 (2010) 021501 [arXiv:0912.3606] [INSPIRE].
Ó.J.C. Dias, G.S. Hartnett and J.E. Santos, Quasinormal modes of asymptotically flat rotating black holes, Class. Quant. Grav. 31 (2014) 245011 [arXiv:1402.7047] [INSPIRE].
Ó.J.C. Dias, P. Figueras, R. Monteiro, J.E. Santos and R. Emparan, Instability and new phases of higher-dimensional rotating black holes, Phys. Rev. D 80 (2009) 111701 [arXiv:0907.2248] [INSPIRE].
Ó.J.C. Dias, P. Figueras, R. Monteiro, H.S. Reall and J.E. Santos, An instability of higher-dimensional rotating black holes, JHEP 05 (2010) 076 [arXiv:1001.4527] [INSPIRE].
Ó.J.C. Dias, P. Figueras, R. Monteiro and J.E. Santos, Ultraspinning instability of rotating black holes, Phys. Rev. D 82 (2010) 104025 [arXiv:1006.1904] [INSPIRE].
M. Durkee and H.S. Reall, Perturbations of higher-dimensional spacetimes, Class. Quant. Grav. 28 (2011) 035011 [arXiv:1009.0015] [INSPIRE].
K. Murata, Instability of higher dimensional extreme black holes, Class. Quant. Grav. 30 (2013) 075002 [arXiv:1211.6903] [INSPIRE].
R. Emparan and R.C. Myers, Instability of ultra-spinning black holes, JHEP 09 (2003) 025 [hep-th/0308056] [INSPIRE].
B. Gwak and B.-H. Lee, Instability of rotating anti-de Sitter black holes, Phys. Rev. D 91 (2015) 064020 [arXiv:1405.2803] [INSPIRE].
B. Gwak, B.-H. Lee and D. Ro, Instability of Charged Anti-de Sitter Black Holes, arXiv:1509.03493 [INSPIRE].
W.-K. Ahn, B. Gwak, B.-H. Lee and W. Lee, Instability of Black Holes with a Gauss-Bonnet Term, Eur. Phys. J. C 75 (2015) 372 [arXiv:1412.4189] [INSPIRE].
S.W. Hawking, Gravitational radiation from colliding black holes, Phys. Rev. Lett. 26 (1971) 1344 [INSPIRE].
L.I. Schiff, Motion of a Gyroscope According to Einstein’s Theory of Gravitation, Proc. Nat. Acad. Sci. 46 (1960) 871 [INSPIRE].
B. Mashhoon, Particles with spin in a gravitational field, J. Math. Phys. 12 (1971) 1075 [INSPIRE].
D.C. Wilkins, General equation for the precession of a gyroscope, Ann. Phys. 61 (1970) 277.
R.M. Wald, Gravitational spin interaction, Phys. Rev. D 6 (1972) 406 [INSPIRE].
J. Majar and B. Mikoczi, Second order spin effects in the spin precession of compact binaries, Phys. Rev. D 86 (2012) 064028 [INSPIRE].
M. Zilhão, V. Cardoso, C. Herdeiro, L. Lehner and U. Sperhake, Collisions of oppositely charged black holes, Phys. Rev. D 89 (2014) 044008 [arXiv:1311.6483] [INSPIRE].
C.A.R. Herdeiro, C. Rebelo, M. Zilhão and M.S. Costa, A Double Myers-Perry Black Hole in Five Dimensions, JHEP 07 (2008) 009 [arXiv:0805.1206] [INSPIRE].
R. Plyatsko and M. Fenyk, Highly relativistic spin-gravity coupling for fermions, Phys. Rev. D 91 (2015) 064033 [arXiv:1503.08415] [INSPIRE].
G. d’Ambrosi, S. Satish Kumar, J. van de Vis and J. van Holten, Spinning bodies in curved spacetime, Phys. Rev. D 93 (2016) 044051 [arXiv:1511.05454] [INSPIRE].
D.M. Eardley and S.B. Giddings, Classical black hole production in high-energy collisions, Phys. Rev. D 66 (2002) 044011 [gr-qc/0201034] [INSPIRE].
U. Sperhake, V. Cardoso, F. Pretorius, E. Berti and J.A. Gonzalez, The High-energy collision of two black holes, Phys. Rev. Lett. 101 (2008) 161101 [arXiv:0806.1738] [INSPIRE].
F.S. Coelho, C. Herdeiro and M.O.P. Sampaio, Radiation from a D-dimensional collision of shock waves: a remarkably simple fit formula, Phys. Rev. Lett. 108 (2012) 181102 [arXiv:1203.5355] [INSPIRE].
J. Hennig and G. Neugebauer, Collisions of rigidly rotating disks of dust in general relativity, Phys. Rev. D 74 (2006) 064025 [gr-qc/0606031] [INSPIRE].
J. Hennig, G. Neugebauer and M. Ansorg, Thermodynamic description of inelastic collisions in general relativity, Astrophys. J. 663 (2007) 450 [gr-qc/0701131] [INSPIRE].
L. Smarr, A. Cadez, B.S. DeWitt and K. Eppley, Collision of Two Black Holes: Theoretical Framework, Phys. Rev. D 14 (1976) 2443 [INSPIRE].
L. Smarr, Gravitational Radiation from Distant Encounters and from Headon Collisions of Black Holes: The Zero Frequency Limit, Phys. Rev. D 15 (1977) 2069 [INSPIRE].
L. Smarr and J.W. York Jr., Kinematical conditions in the construction of space-time, Phys. Rev. D 17 (1978) 2529 [INSPIRE].
H. Witek et al., Numerical relativity for D dimensional space-times: head-on collisions of black holes and gravitational wave extraction, Phys. Rev. D 82 (2010) 104014 [arXiv:1006.3081] [INSPIRE].
P. Anninos, D. Hobill, E. Seidel, L. Smarr and W.-M. Suen, The Collision of two black holes, Phys. Rev. Lett. 71 (1993) 2851 [gr-qc/9309016] [INSPIRE].
P. Anninos et al., Dynamics of apparent and event horizons, Phys. Rev. Lett. 74 (1995) 630 [gr-qc/9403011] [INSPIRE].
P. Anninos and S. Brandt, Headon collision of two unequal mass black holes, Phys. Rev. Lett. 81 (1998) 508 [gr-qc/9806031] [INSPIRE].
M. Zilhão et al., Numerical relativity for D dimensional axially symmetric space-times: formalism and code tests, Phys. Rev. D 81 (2010) 084052 [arXiv:1001.2302] [INSPIRE].
H. Witek, V. Cardoso, L. Gualtieri, C. Herdeiro, U. Sperhake and M. Zilhão, Head-on collisions of unequal mass black holes in D = 5 dimensions, Phys. Rev. D 83 (2011) 044017 [arXiv:1011.0742] [INSPIRE].
H. Witek et al., Higher dimensional Numerical Relativity: code comparison, Phys. Rev. D 90 (2014) 084014 [arXiv:1406.2703] [INSPIRE].
C. Reisswig, N.T. Bishop, D. Pollney and B. Szilagyi, Unambiguous determination of gravitational waveforms from binary black hole mergers, Phys. Rev. Lett. 103 (2009) 221101 [arXiv:0907.2637] [INSPIRE].
H. Bantilan and P. Romatschke, Simulation of Black Hole Collisions in Asymptotically Anti-de Sitter Spacetimes, Phys. Rev. Lett. 114 (2015) 081601 [arXiv:1410.4799] [INSPIRE].
W. Bednarek and P. Banasinski, Non-thermal radiation from collisions of compact objects with intermediate scale jets in active galaxies, Astrophys. J. 807 (2015) 168 [arXiv:1506.01181] [INSPIRE].
K. Hirotani and H.-Y. Pu, Energetic Gamma Radiation from Rapidly Rotating Black Holes, Astrophys. J. 818 (2016) 50 [arXiv:1512.05026] [INSPIRE].
U. Sperhake, E. Berti, V. Cardoso and F. Pretorius, Gravity-dominated unequal-mass black hole collisions, Phys. Rev. D 93 (2016) 044012 [arXiv:1511.08209] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1603.02103
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Gwak, B., Lee, BH. The upper bound of radiation energy in the Myers-Perry black hole collision. J. High Energ. Phys. 2016, 79 (2016). https://doi.org/10.1007/JHEP07(2016)079
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2016)079