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Carleo, Amodio; Lambiase, Gaetano; Övgün, Ali

Non-linear electrodynamics in Blandford-Znajek energy extraction. (English) Zbl 07771932

Ann. Phys., Berlin 535, No. 5, Article ID 2200635, 11 p. (2023).
Summary: Non-linear electrodynamics (NLED) is a generalization of Maxwell’s electrodynamics for strong fields. It has significant implications for the study of black holes and cosmology and has been extensively studied in the literature, extending from quantum to cosmological contexts. In this work, two new ways to investigate these non-linear theories are investigated. First, the Blandford-Znajek mechanism is analyzed in light of this promising theoretical context, providing the general form of the extracted power up to second order in the black hole spin parameter \(a\). It is found that, depending on the NLED model, the emitted power can be extremely increased or decreased, and that the magnetic field lines around the black hole seem to become vertical quickly. Considering only separated solutions, it is found that no monopole solutions exist and this could have interesting astrophysical consequences (not considered here). Last but not least, it is attempted to confine the NLED parameters by inducing the amplification of primordial magnetic fields (“seeds”), thus admitting non-linear theories already during the early stages of the Universe. However, the latter approach proves to be useful for NLED research only in certain models. These (analytical) results emphasize that the behavior of non-linear electromagnetic phenomena strongly depends on the physical context and that only a power-law model seems to have any chance to compete with Maxwell.
© 2023 The Authors. Annalen der Physik published by Wiley-VCH GmbH

Cited in 2 Documents

MSC:

81-XX Quantum theory

Keywords:

black holes; Blandford-Znajek; energy extraction; non-linear electrodynamics
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[1] M.Born, Nature1933, 132, 282. · Zbl 0007.23402
[2] M.Born, L.Infeld, Proc. R. Soc. London, Ser. A1934, 144, 425. · Zbl 0008.42203
[3] G. W.Gibbons, AIP Conf. Proc.2001, 589, 324.
[4] E. S.Fradkin, A. A.Tseytlin, Phys. Lett. B1985, 163, 123. · Zbl 0967.81534
[5] J. M.Davila, C.Schubert, M. A.Trejo, Int. J. Mod. Phys. A2014, 29, 1450174. · Zbl 1306.81310
[6] J.Ellis, N. E.Mavromatos, T.You, Phys. Rev. Lett.2017, 118, 261802.
[7] P.Niau Akmansoy, L. G.Medeiros, Eur. Phys. J. C2018, 78, 143.
[8] P.Niau Akmansoy, L. G.Medeiros, Phys. Rev. D2019, 99, 115005.
[9] M. J.Neves, J. B.deOliveira, L. P. R.Ospedal, J. A.Helayël‐Neto, Phys. Rev. D2021, 104, 015006.
[10] M. J.Neves, L. P. R.Ospedal, J. A.Helayël‐Neto, P.Gaete, Eur. Phys. J. C2022, 82, 327.
[11] P.De Fabritiis, P. C.Malta, J. A.Helayël‐Neto, Phys. Rev. D2022, 105, 016007.
[12] W.Heisenberg, H.Euler, Z. Phys.1936, 98, 714. · Zbl 0013.18503
[13] S. I.Kruglov, Phys. Rev. D2007, 75, 117301.
[14] S.Kruglov, Ann. Phys.2015, 353, 299. · Zbl 1343.78001
[15] S. I.Kruglov, Ann. Phys.2015, 527, 397. · Zbl 1339.78003
[16] S. I.Kruglov, Eur. Phys. J. C2015, 75, 88.
[17] S. I.Kruglov, Int. J. Geom. Methods Mod. Phys.2015, 12, 1550073. · Zbl 1329.83116
[18] S. I.Kruglov, Phys. Rev. D2015, 92, 123523.
[19] S. I.Kruglov, Int. J. Mod. Phys. D2016, 25, 1640002. · Zbl 1351.83070
[20] S. I.Kruglov, Phys. Rev. D2016, 94, 044026.
[21] S. I.Kruglov, Ann. Phys.2016, 528, 588. · Zbl 1350.83010
[22] S. I.Kruglov, Ann. Phys.2017, 383, 550.
[23] S. I.Kruglov, Ann . Phys.2017, 378, 59. · Zbl 1367.83053
[24] S. I.Kruglov, Ann. Phys.2017, 529, 1700073. · Zbl 1375.83029
[25] Z.‐Y.Fan, X.Wang, Phys. Rev. D2016, 94, 124027.
[26] H. J.Mosquera Cuesta, G.Lambiase, Phys. Rev. D2009, 80, 023013.
[27] H. J.Mosquera Cuesta, G.Lambiase, J. Cosmol. Astropart. Phys.2011, 03, 033.
[28] H. J.Mosquera Cuesta, G.Lambiase, Int. J. Mod. Phys. D2009, 18, 435. · Zbl 1173.83306
[29] C.Corda, H. J.Mosquera Cuesta, Astropart. Phys.2011, 34, 587.
[30] H. J.Mosquera Cuesta, J. M.Salim, Mon. Not. R. Astron. Soc.2004, 354, L55.
[31] H. J.Mosquera Cuesta, J. M.Salim, Astrophys. J.2004, 608, 925.
[32] H. J.Mosquera Cuesta, J. A.deFreitas Pacheco, J. M.Salim, Int. J. Mod. Phys. A2006, 21, 43. · Zbl 1102.83001
[33] J. P.Mbelek, H. J.Mosquera Cuesta, M.Novello, J. M.Salim, EPL2007, 77, 19001.
[34] J. P.Mbelek, H. J.Mosquera Cuesta, Mon. Not. R. Astron. Soc.2008, 389, 199.
[35] N.Breton, R.Garcia‐Salcedo, arXiv:1708.07006, 2007.
[36] G.Panotopoulos, Chin. J. Phys.2021, 69, 295. · Zbl 07833885
[37] G.Panotopoulos, A.Rincón, Int. J. Mod. Phys. D2017, 27, 1850034.
[38] B.Toshmatov, Z.Stuchlík, J.Schee, B.Ahmedov, Phys. Rev. D2018, 97, 084058.
[39] Z.Stuchlík, J.Schee, Eur. Phys. J. C2019, 79, 44.
[40] J.Rayimbaev, D.Bardiev, F.Abdulxamidov, A.Abdujabbarov, B.Ahmedov, Universe2022, 8, 549.
[41] B.Toshmatov, B.Ahmedov, A.Abdujabbarov, Z.Stuchlik, Phys. Rev. D2014, 89, 104017.
[42] A.Abdujabbarov, M.Amir, B.Ahmedov, S. G.Ghosh, Phys. Rev. D2016, 93, 104004.
[43] B.Toshmatov, Z.Stuchlík, B.Ahmedov, Phys. Rev. D2017, 95, 084037.
[44] Z.Stuchlík, J.Schee, Int. J. Mod. Phys. D2014, 24, 1550020.
[45] D. H.Delphenich, arXiv:hep‐th/0610088, 2006.
[46] J.Lundin, G.Brodin, M.Marklund, Phys. Plasmas2006, 13, 102102.
[47] E.Lundstrom, G.Brodin, J.Lundin, M.Marklund, R.Bingham, J.Collier, J. T.Mendonca, P.Norreys, Phys. Rev. Lett.2006, 96, 083602.
[48] A.Ohnishi, N.Yamamoto, arXiv:1402.4760, 2014.
[49] Y.Akamatsu, N.Yamamoto, Phys. Rev. Lett.2013, 111, 052002.
[50] A.Rincon, P. A.Gonzalez, G.Panotopoulos, J.Saavedra, Y.Vasquez, Eur. Phys. J. Plus2022, 137, 1278.
[51] P. A.González, A.Rincón, J.Saavedra, Y.Vásquez, Phys. Rev. D2021, 104, 084047.
[52] A.Rincón, E.Contreras, P.Bargueño, B.Koch, G.Panotopoulos, Eur. Phys. J. C2018, 78, 641.
[53] A.Rincón, E.Contreras, P.Bargueño, B.Koch, G.Panotopoulos, A.Hernández‐Arboleda, Eur. Phys. J. C2017, 77, 494.
[54] J.Diaz‐alonso, D.Rubiera‐Garcia, arXiv:1301.3648, 2013.
[55] H. J.Mosquera Cuesta, G.Lambiase, J. P.Pereira, Phys. Rev. D2017, 95, 025011.
[56] M.Okyay, A.Övgün, J. Cosmol. Astropart. Phys.2022, 2022, 009.
[57] A.Övgün, Phys. Rev. D2019, 99, 104075.
[58] Y.Kumaran, A.Övgün, Symmetry2022, 14, 2054.
[59] R. C.Pantig, L.Mastrototaro, G.Lambiase, A.Övgün, Eur. Phys. J. C2022, 82, 1155.
[60] W.Javed, M.Aqib, A.Övgün, Phys. Lett. B2022, 829, 137114. · Zbl 1496.83029
[61] X.‐M.Kuang, B.Liu, A.Övgün, Eur. Phys. J. C2018, 78, 840.
[62] W.Javed, J.Abbas, A.Övgün, Eur. Phys. J. C2019, 79, 694.
[63] W.Javed, A.Hamza, A.Övgün, Phys. Rev. D2020, 101, 103521.
[64] H.El Moumni, K.Masmar, A.Övgün, Int. J. Geom. Methods Mod. Phys.2022, 19, 2250094. · Zbl 1537.83011
[65] A.Uniyal, R. C.Pantig, A.Övgün, Phys. Dark Universe2023, 40, 101178.
[66] K.Jusufi, A.Övgün, J.Saavedra, Y.Vásquez, P. A.González, Phys. Rev. D2018, 97, 124024.
[67] M.Halilsoy, A.Ovgun, S. H.Mazharimousavi, Eur. Phys. J. C2014, 74, 2796.
[68] A.Allahyari, M.Khodadi, S.Vagnozzi, D. F.Mota, J. Cosmol. Astropart. Phys.2020, 02, 003.
[69] S.Vagnozzi, R.Roy, Y.‐D.Tsai, L.Visinelli, M.Afrin, A.Allahyari, P.Bambhaniya, D.Dey, S. G.Ghosh, P. S.Joshi, K.Jusufi, M.Khodadi, R. K.Walia, A.Övgün, C.Bambi, arXiv:2205.07787, 2022.
[70] R.Garcia‐Salcedo, N.Breton, Int. J. Mod. Phys. A2000, 15, 4341. · Zbl 0977.83125
[71] H. B.Benaoum, G.Leon, A.Ovgun, H.Quevedo, arXiv:2206.13157, 2022.
[72] A.Övgün, Eur. Phys. J. C2017, 77, 105.
[73] A.Övgün, G.Leon, J.Magaña, K.Jusufi, Eur. Phys. J. C2018, 78, 462.
[74] G.Otalora, A.Övgün, J.Saavedra, N.Videla, J. Cosmol. Astropart. Phys.2018, 06, 003.
[75] G. W.Joseph, A.Övgün, Indian J. Phys.2022, 96, 1861.
[76] H. B.Benaoum, A.Ovgun, Classical Quantum Gravity2021, 38, 135019. · Zbl 1481.83096
[77] K. E.Kunze, Plasma Phys. Controlled Fusion2013, 55, 124026.
[78] R.Durrer, A.Neronov, Astron. Astrophys. Rev.2013, 21, 62.
[79] K. E.Kunze, Phys. Rev. D2008, 77, 023530.
[80] L.Campanelli, P.Cea, G. L.Fogli, L.Tedesco, Phys. Rev. D2008, 77, 043001.
[81] M.Gasperini, M.Giovannini, G.Veneziano, Phys. Rev. Lett.1995, 75, 3796.
[82] K.Bamba, C. Q.Geng, S. H.Ho, J. Cosmol. Astropart. Phys.2008, 2008, 013.
[83] M. S.Turner, L. M.Widrow, Phys. Rev. D1988, 37, 2743.
[84] R.Opher, U. F.Wichoski, Phys. Rev. Lett.1997, 78, 787.
[85] K.Bamba, C.‐Q.Geng, C.‐C.Lee, J. Cosmol. Astropart. Phys.2010, 2010, 021.
[86] F. D.Mazzitelli, F. M.Spedalieri, Phys. Rev. D1995, 52, 6694.
[87] S.Matarrese, S.Mollerach, A.Notari, A.Riotto, Phys. Rev. D2005, 71, 043502.
[88] C. G.Tsagas, P. K.Dunsby, M.Marklund, Phys. Lett. B2003, 561, 17.
[89] O.Bertolami, D.Mota, Phys. Lett. B1999, 455, 96.
[90] T.Vachaspati, A.Vilenkin, Phys. Rev. Lett.1991, 67, 1057.
[91] M.Joyce, M.Shaposhnikov, Phys. Rev. Lett.1997, 79, 1193.
[92] A.Dolgov, J.Silk, Phys. Rev. D1993, 47, 3144.
[93] A. D.Dolgov, Phys. Rev. D1993, 48, 2499.
[94] V. B.Semikoz, D. D.Sokoloff, Phys. Rev. Lett.2004, 92, 131301.
[95] S.Capozziello, A.Carleo, G.Lambiase, J. Cosmol. Astropart. Phys.2022, 10, 020. · Zbl 1512.83048
[96] H. J. M.Cuesta, G.Lambiase, Phys. Rev. D2009, 80, 2.
[97] S. S.Komissarov, Mon. Not. R. Astron. Soc.2005, 359, 801.
[98] E.NAKAR, Phys. Rep.2007, 442, 166.
[99] R. D.Blandford, R. L.Znajek, Mon. Not. R. Astron. Soc.1977, 179, 433.
[100] A.Tchekhovskoy, R.Narayan, J. C.McKinney, Astrophys. J.2010, 711, 50.
[101] H. K.Lee, R. A. M. J.Wijers, G. E.Brown, Phys. Rept.2000, 325, 83.
[102] A.Tchekhovskoy, J. C.McKinney, R.Narayan, Mon. Not. R. Astron. Soc.2008, 388, 551.
[103] S. S.Komissarov, M. V.Barkov, Mon. Not. R. Astron. Soc.2009, 397, 1153.
[104] R.Ruffini, J. R.Wilson, Phys. Rev. D1975, 12, 2959.
[105] L.Comisso, F. A.Asenjo, Phys. Rev. D2021, 103, 2.
[106] A.Carleo, G.Lambiase, L.Mastrototaro, Eur. Phys. J. C2022, 82, 776.
[107] R. M.Wald, Astrophys. J.1974, 191, 231.
[108] Z.Stuchlík, M.Kološ, A.Tursunov, Universe2021, 7, 11.
[109] A.Tursunov, Z.Stuchlík, M.Kološ, N.Dadhich, B.Ahmedov, Astrophys. J.2020, 895, 14.
[110] N.Dadhich, arXiv:1210.1041, 2012.
[111] N.Dadhich, A.Tursunov, B.Ahmedov, Z.Stuchlík, Mon. Not. R. Astron. Soc.: Lett.2018, 478, L89.
[112] V.Sharma, S.Iyyani, D.Bhattacharya, Astrophys. J.2021, 908, L2.
[113] M.Takahashi, M.Kino, H.‐Y.Pu, Phys. Rev. D2021, 104, 10.
[114] A. R.King, J. E.Pringle, Astrophys. J. Lett.2021, 918, L22.
[115] S. S.Komissarov, Mon. Not. R. Astron. Soc.2021, 512, 2798.
[116] S. S.Komissarov, Mon. Not. R. Astron. Soc.2005, 359, 801.
[117] I.Contopoulos, A.Nathanail, A.Strantzalis, Galaxies2017, 5, 2.
[118] R. J.Ruffini, in The Ninth Marcel Grossmann Meeting, World Scientific Publishing Company, Singapore2002, pp. 347-379. · Zbl 1040.83026
[119] J. C.McKinney, Mon. Not. R. Astron. Soc.2006, 368, 1561.
[120] J. F.Steiner, J. E.McClintock, R.Narayan, Astrophys. J.2012, 762, 104.
[121] J. C.McKinney, C. F.Gammie, Astrophys. J.2004, 611, 977.
[122] Notice that here we use a different metric signature than ref. [121] and that in ref. [99] Kerr coordinates are used.
[123] \(X=\frac{1}{2}{(|\mathbf{B}|}^2-{|\mathbf{E}|}^2)\).
[124] Notice that our definition for \({B}_{\phi}\) differs from that of ref. [99] by a factor \(\sqrt{-g} \) (as assumed in ref. [121]).
[125] P.Ghosh, Mon. Not. R. Astron. Soc.2000, 315, 89.
[126] A solution for \({A}_{\phi}^{(2)}\) requires a second order equation. See Appendix.
[127] Generally, \({L}_X\) is an even function of a, that is, \({L}_X={L}_X^0+{a}^2{L}_X^2+\mathcal{O}({a}^4)\). It is essential that \({L}_X^0\ne 0\) in order to have a solution.
[128] One in principle can generalize to higher orders as done, for example, in ref. [125].
[129] The so‐called Kruglov model,[14] for example, is not separable, while the Born- Infeld one reduces to a power‐law.
[130] The logarithmic singularity, also present in the linear limit, simply means that solutions are valid in regions of space which exclude event horizon.
[131] S. S.Komissarov, Mon. Not. R. Astron. Soc.2001, 326, L41.
[132] A.Nathanail, I.Contopoulos, Astrophys. J.2014, 788, 186.
[133] R. F.Penna, R.Narayan, A.Są dowski, Mon. Not. R. Astron. Soc.2013, 436, 3741.
[134] A purely radial magnetic field (monopole), although not realistic, is still considered today being the simplest configuration to implement,[131] both numerically and analytically.
[135] The (separable) paraboloidal Schwarzschild solution in linear theory goes like \({A}_{\phi}^{(0)}\approx (\cos\theta -1)(r+2\ln(r-2))\) as reported in ref. [125].
[136] Expressions for P and \({P}^{\text{NLED}}\) are at fault only for a constant depending on the field configuration (monopole, paraboloidal, etc.). We assume that they are of the same order in both cases, as it is plausible.
[137] G.Pei, S.Nampalliwar, C.Bambi, M. J.Middleton, Eur. Phys. J. C2016, 76, 10.
[138] A power‐law electromagnetic model seems capable of extracting much more energy than models employing Kerr metric deformations. For example, in the case of a Johannsen metric, the extracted energy is no more than ≈10 times larger.^[137] In our framework, the ratio \({P}^{\text{NLED}}/P\) can exceed 10^4 (see Figure 3).
[139] R. P.Eatough, H.Falcke, R.Karuppusamy, K. J.Lee, D. J.Champion, E. F.Keane, G.Desvignes, D. H. F. M.Schnitzeler, L. G.Spitler, M.Kramer, B.Klein, C.Bassa, G. C.Bower, A.Brunthaler, I.Cognard, A. T.Deller, P. B.Demorest, P. C. C.Freire, A.Kraus, A. G.Lyne, A.Noutsos, B.Stappers, N.Wex, Nature2013, 501, 391.
[140] M.Liska, A.Tchekhovskoy, E.Quataert, Mon. Not. R. Astron. Soc.2020, 494, 3656.
[141] Event Horizon Telescope Collaboration, Astrophys. J.2021, 910, L13.
[142] R.Kothari, M. V. S.Saketh, P.Jain, Phys. Rev. D2020, 102, 024008.
[143] M.Gasperini, M.Giovannini, G.Veneziano, Phys. Rev. Lett.1995, 75, 3796.
[144] K.Atmjeet, I.Pahwa, T.Seshadri, K.Subramanian, Phys. Rev. D2014, 89, 6.
[145] We are assuming a scale factor of the type \(a(\eta )={c}_s{\eta}^s\), where \({c}_s\) is the Hubble constant for the specific primordial era. Notice that the values of s are those of general relativity; changing the gravitational sector in the action (Equation (37)) leads to different s values. See for example.^[95] This is the only point in which, in a minimal approach, gravity comes into play.
[146] A Born- Infeld model,^[2, 1] does not allow either pseudo‐power‐law or power‐law solutions. Expanding the Lagrangian in powers of X, however, leads to a power‐law model with \(\delta =2\) studied in ref. [96], and hence to the same solutions, which, however, seems to exclude power‐law Lagrangian \({L}_{\text{NLED}}=- CX -\gamma{X}^{\delta}\) with \(\delta >2\).
[147] R.Konoplya, J.Kunz, A.Zhidenko, J. Cosmol. Astropart. Phys.2021, 2021, 002.
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