×

Higher-order Skyrme hair of black holes. (English) Zbl 1391.83060

Summary: Higher-order derivative terms are considered as replacement for the Skyrme term in an Einstein-Skyrme-like model in order to pinpoint which properties are necessary for a black hole to possess stable static scalar hair. We find two new models able to support stable black hole hair in the limit of the Skyrme term being turned off. They contain 8 and 12 derivatives, respectively, and are roughly the Skyrme-term squared and the so-called BPS-Skyrme-term squared. In the twelfth-order model we find that the lower branches, which are normally unstable, become stable in the limit where the Skyrme term is turned off. We check this claim with a linear stability analysis. Finally, we find for a certain range of the gravitational coupling and horizon radius, that the twelfth-order model contains 4 solutions as opposed to 2. More surprisingly, the lowest part of the would-be unstable branch turns out to be the stable one of the 4 solutions.

MSC:

83C57 Black holes
35Q51 Soliton equations
81T10 Model quantum field theories
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Lückock, H.; Moss, I., Black holes have skyrmion hair, Phys. Lett., B 176, 341, (1986) · doi:10.1016/0370-2693(86)90175-9
[2] Glendenning, NK; Kodama, T.; Klinkhamer, FR, Skyrme topological soliton coupled to gravity, Phys. Rev., D 38, 3226, (1988)
[3] Droz, S.; Heusler, M.; Straumann, N., New black hole solutions with hair, Phys. Lett., B 268, 371, (1991) · doi:10.1016/0370-2693(91)91592-J
[4] Heusler, M.; Droz, S.; Straumann, N., Stability analysis of selfgravitating skyrmions, Phys. Lett., B 271, 61, (1991) · doi:10.1016/0370-2693(91)91278-4
[5] Heusler, M.; Droz, S.; Straumann, N., Linear stability of Einstein Skyrme black holes, Phys. Lett., B 285, 21, (1992) · doi:10.1016/0370-2693(92)91294-J
[6] Bizon, P.; Chmaj, T., Gravitating skyrmions, Phys. Lett., B 297, 55, (1992) · doi:10.1016/0370-2693(92)91069-L
[7] Volkov, MS; Gal’tsov, DV, Gravitating non-abelian solitons and black holes with Yang-Mills fields, Phys. Rept., 319, 1, (1999) · doi:10.1016/S0370-1573(99)00010-1
[8] N. Shiiki and N. Sawado, Black holes with Skyrme hair, gr-qc/0501025 [INSPIRE]. · Zbl 1153.83367
[9] Skyrme, THR, A nonlinear field theory, Proc. Roy. Soc. Lond., A 260, 127, (1961) · Zbl 0102.22605 · doi:10.1098/rspa.1961.0018
[10] Skyrme, THR, A unified field theory of mesons and baryons, Nucl. Phys., 31, 556, (1962) · doi:10.1016/0029-5582(62)90775-7
[11] Witten, E., Global aspects of current algebra, Nucl. Phys., B 223, 422, (1983) · doi:10.1016/0550-3213(83)90063-9
[12] Witten, E., Current algebra, baryons and quark confinement, Nucl. Phys., B 223, 433, (1983) · doi:10.1016/0550-3213(83)90064-0
[13] Gudnason, SB; Nitta, M.; Sawado, N., Gravitating BPS skyrmions, JHEP, 12, 013, (2015) · Zbl 1388.81413
[14] C. Adam, O. Kichakova, Ya. Shnir and A. Wereszczynski, Hairy black holes in the general Skyrme model, Phys. Rev.D 94 (2016) 024060 [arXiv:1605.07625] [INSPIRE]. · Zbl 1349.83044
[15] Gudnason, SB; Nitta, M.; Sawado, N., Black hole skyrmion in a generalized Skyrme model, JHEP, 09, 055, (2016) · Zbl 1390.83202 · doi:10.1007/JHEP09(2016)055
[16] Adkins, GS; Nappi, CR, Stabilization of chiral solitons via vector mesons, Phys. Lett., B 137, 251, (1984) · doi:10.1016/0370-2693(84)90239-9
[17] Jackson, A.; Jackson, AD; Goldhaber, AS; Brown, GE; Castillejo, LC, A modified skyrmion, Phys. Lett., B 154, 101, (1985) · doi:10.1016/0370-2693(85)90566-0
[18] Adam, C.; Sanchez-Guillen, J.; Wereszczynski, A., A Skyrme-type proposal for baryonic matter, Phys. Lett., B 691, 105, (2010) · doi:10.1016/j.physletb.2010.06.025
[19] Adam, C.; Sanchez-Guillen, J.; Wereszczynski, A., A BPS Skyrme model and baryons at large N_{c}, Phys. Rev., D 82, (2010) · Zbl 1370.81101
[20] Gudnason, SB; Nitta, M.; Sasaki, S., A supersymmetric Skyrme model, JHEP, 02, 074, (2016) · Zbl 1388.81236 · doi:10.1007/JHEP02(2016)074
[21] Gudnason, SB; Nitta, M.; Sasaki, S., Topological solitons in the supersymmetric Skyrme model, JHEP, 01, 014, (2017) · Zbl 1373.83078 · doi:10.1007/JHEP01(2017)014
[22] Gudnason, SB; Nitta, M., Incarnations of skyrmions, Phys. Rev., D 90, (2014)
[23] Gudnason, SB; Nitta, M., Fractional skyrmions and their molecules, Phys. Rev., D 91, (2015)
[24] Adam, C.; Haberichter, M.; Romanczukiewicz, T.; Wereszczynski, A., Radial vibrations of BPS skyrmions, Phys. Rev., D 94, (2016) · Zbl 1388.81254
[25] Adam, C.; Sanchez-Guillen, J.; Wereszczynski, A., On the spin excitation energy of the nucleon in the Skyrme model, Int. J. Mod. Phys., E 25, 1650097, (2016) · Zbl 1370.81101 · doi:10.1142/S021830131650097X
[26] Gudnason, SB; Zhang, B.; Ma, N., Generalized Skyrme model with the loosely bound potential, Phys. Rev., D 94, 125004, (2016)
[27] Adam, C.; Haberichter, M.; Romanczukiewicz, T.; Wereszczynski, A., Roper resonances and quasi-normal modes of skyrmions, JHEP, 03, 023, (2018) · Zbl 1388.81254 · doi:10.1007/JHEP03(2018)023
[28] Gudnason, SB; Nitta, M., A higher-order Skyrme model, JHEP, 09, 028, (2017) · Zbl 1382.83111 · doi:10.1007/JHEP09(2017)028
[29] L. Marleau, The Skyrme model and higher order terms, Phys. Lett.B 235 (1990) 141 [Erratum ibid.B 244 (1990) 580] [INSPIRE].
[30] Marleau, L., Modifying the Skyrme model: pion mass and higher derivatives, Phys. Rev., D 43, 885, (1991)
[31] Marleau, L., All orders skyrmions, Phys. Rev., D 45, 1776, (1992) · Zbl 0967.81063
[32] N. Shiiki and N. Sawado, Black hole skyrmions with negative cosmological constant, Phys. Rev.D 71 (2005) 104031 [gr-qc/0502107] [INSPIRE]. · Zbl 1153.83367
[33] N. Shiiki and N. Sawado, Regular and black hole solutions in the Einstein-Skyrme theory with negative cosmological constant, Class. Quant. Grav.22 (2005) 3561 [gr-qc/0503123] [INSPIRE]. · Zbl 1153.83367
[34] Perapechka, I.; Shnir, Y., Generalized skyrmions and hairy black holes in asymptotically ads_{4} spacetime, Phys. Rev., D 95, (2017)
[35] Brihaye, Y.; Delsate, T., Skyrmion and Skyrme-black holes in de Sitter spacetime, Mod. Phys. Lett., A 21, 2043, (2006) · doi:10.1142/S0217732306021426
[36] Zajac, S., Late-time evolution of the gravitating skyrmion, Acta Phys. Polon., B 40, 1617, (2009)
[37] Zajac, S., Late-time tails of self-gravitating skyrmions, Acta Phys. Polon., B 42, 249, (2011) · doi:10.5506/APhysPolB.42.249
[38] N. Shiiki, N. Sawado and S. Oryu, Collective quantisation of a gravitating skyrmion, Phys. Rev.D 70 (2004) 114023 [hep-ph/0409054] [INSPIRE].
[39] N. Sawado and N. Shiiki, Axially symmetric black hole skyrmions, eConfC 0306234 (2003) 1442 [gr-qc/0307115] [INSPIRE]. · Zbl 1097.83521
[40] N. Sawado, N. Shiiki, K.-I. Maeda and T. Torii, Regular and black hole skyrmions with axisymmetry, Gen. Rel. Grav.36 (2004) 1361 [gr-qc/0401020] [INSPIRE]. · Zbl 1048.83015
[41] Sato, H.; Sawado, N.; Shiiki, N., Collective quantization of axially symmetric gravitating B = 2 skyrmion, Phys. Rev., D 75, (2007)
[42] T. Ioannidou, B. Kleihaus and J. Kunz, Spinning gravitating skyrmions, Phys. Lett.B 643 (2006) 213 [gr-qc/0608110] [INSPIRE]. · Zbl 1248.83017
[43] Perapechka, I.; Shnir, Y., Spinning gravitating skyrmions in a generalized Einstein-Skyrme model, Phys. Rev., D 96, 125006, (2017)
[44] Ya. Shnir, Gravitating sphalerons in the Skyrme model, Phys. Rev.D 92 (2015) 085039 [arXiv:1508.06507] [INSPIRE].
[45] C. Adam, T. Romanczukiewicz, M. Wachla and A. Wereszczynski, Exactly solvable gravitating perfect fluid solitons in (2 + 1) dimensions, arXiv:1802.07278 [INSPIRE]. · Zbl 1395.83077
[46] M. Wachla, Gravitating gauged BPS baby skyrmions, arXiv:1803.10690 [INSPIRE]. · Zbl 1390.83202
[47] Brihaye, Y.; Herdeiro, C.; Radu, E.; Tchrakian, DH, Skyrmions, Skyrme stars and black holes with Skyrme hair in five spacetime dimension, JHEP, 11, 037, (2017) · Zbl 1383.83046 · doi:10.1007/JHEP11(2017)037
[48] F.R. Klinkhamer and J.M. Queiruga, Antigravity from a spacetime defect, arXiv:1803.09736 [INSPIRE]. · Zbl 1391.83029
[49] Adam, C.; Naya, C.; Sanchez-Guillen, J.; Vazquez, R.; Wereszczynski, A., BPS skyrmions as neutron stars, Phys. Lett., B 742, 136, (2015) · doi:10.1016/j.physletb.2015.01.027
[50] Adam, C.; Naya, C.; Sanchez-Guillen, J.; Vazquez, R.; Wereszczynski, A., Neutron stars in the bogomol’nyi-Prasad-Sommerfield Skyrme model: mean-field limit versus full field theory, Phys. Rev., C 92, (2015)
[51] Dvali, G.; Gußmann, A., Skyrmion black hole hair: conservation of baryon number by black holes and observable manifestations, Nucl. Phys., B 913, 1001, (2016) · Zbl 1349.83044 · doi:10.1016/j.nuclphysb.2016.10.017
[52] Dvali, G.; Gußmann, A., Aharonov-Bohm protection of black hole’s baryon/skyrmion hair, Phys. Lett., B 768, 274, (2017) · Zbl 1370.83047 · doi:10.1016/j.physletb.2017.03.004
[53] Adam, C.; Naya, C.; Sanchez-Guillen, J.; Speight, JM; Wereszczynski, A., Thermodynamics of the BPS Skyrme model, Phys. Rev., D 90, (2014) · Zbl 1331.81290
[54] Adam, C.; Klähn, T.; Naya, C.; Sanchez-Guillen, J.; Vazquez, R.; Wereszczynski, A., Baryon chemical potential and in-medium properties of BPS skyrmions, Phys. Rev., D 91, 125037, (2015)
[55] Gudnason, SB; Nitta, M., Domain wall skyrmions, Phys. Rev., D 89, (2014)
[56] Gudnason, SB; Nitta, M., Baryonic torii: toroidal baryons in a generalized Skyrme model, Phys. Rev., D 91, (2015)
[57] Gudnason, SB; Nitta, M., Skyrmions confined as beads on a vortex ring, Phys. Rev., D 94, (2016)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.