Abstract
Einstein gravity minimally coupled to a scalar field with a two-parameter Higgs-like self-interaction in three spacetime dimensions is recast in terms of a Chern-Simons form for the algebra g+ ⊕ g− where, depending on the sign of the self-interaction couplings, g± can be so(2, 2), so(3, 1) or iso(2, 1). The field equations can then be expressed through the field strength of non-flat composite gauge fields, and conserved charges are readily obtained from boundary terms in the action that agree with those of standard Chern-Simons theory for pure gravity, but with non-flat connections. Regularity of the fields then amounts to requiring the holonomy of the connections along contractible cycles to be trivial. These conditions are automatically fulfilled for the scalar soliton and allow to recover the Hawking temperature and chemical potential in the case of the rotating hairy black holes presented here, whose entropy can also be obtained by the same formula that holds in the case of a pure Chern-Simons theory. In the conformal (Jordan) frame the theory is described by General Relativity with cosmological constant conformally coupled to a self-interacting scalar field, and its formulation in terms of a Chern-Simons form for suitably composite gauge fields is also briefly addressed.
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References
A. Achúcarro and P.K. Townsend, A Chern-Simons Action for Three-Dimensional anti-de Sitter Supergravity Theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].
E. Witten, (2 + 1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
S. Carlip, Lectures on (2 + 1) dimensional gravity, J. Korean Phys. Soc. 28 (1995) S447 [gr-qc/9503024] [INSPIRE].
O. Coussaert, M. Henneaux and P. van Driel, The Asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant, Class. Quant. Grav. 12 (1995) 2961 [gr-qc/9506019] [INSPIRE].
P. Kraus, Lectures on black holes and the AdS3/CFT2 correspondence, Lect. Notes Phys. 755 (2008) 193 [hep-th/0609074] [INSPIRE].
A. Maloney and E. Witten, Quantum Gravity Partition Functions in Three Dimensions, JHEP 02 (2010) 029 [arXiv:0712.0155] [INSPIRE].
G. Barnich and H.A. González, Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity, JHEP 05 (2013) 016 [arXiv:1303.1075] [INSPIRE].
H. Afshar et al., Soft Heisenberg hair on black holes in three dimensions, Phys. Rev. D 93 (2016) 101503 [arXiv:1603.04824] [INSPIRE].
A. Pérez, D. Tempo and R. Troncoso, Boundary conditions for General Relativity on AdS3 and the KdV hierarchy, JHEP 06 (2016) 103 [arXiv:1605.04490] [INSPIRE].
O. Fuentealba et al., Integrable systems with BMS3 Poisson structure and the dynamics of locally flat spacetimes, JHEP 01 (2018) 148 [arXiv:1711.02646] [INSPIRE].
J. Cotler and K. Jensen, A theory of reparameterizations for AdS3 gravity, JHEP 02 (2019) 079 [arXiv:1808.03263] [INSPIRE].
D. Melnikov, F. Novaes, A. Pérez and R. Troncoso, Lifshitz Scaling, Microstate Counting from Number Theory and Black Hole Entropy, JHEP 06 (2019) 054 [arXiv:1808.04034] [INSPIRE].
H.A. González, J. Matulich, M. Pino and R. Troncoso, Revisiting the asymptotic dynamics of General Relativity on AdS3, JHEP 12 (2018) 115 [arXiv:1809.02749] [INSPIRE].
D. Grumiller and W. Merbis, Near horizon dynamics of three dimensional black holes, SciPost Phys. 8 (2020) 010 [arXiv:1906.10694] [INSPIRE].
E. Ojeda and A. Pérez, Boundary conditions for General Relativity in three-dimensional spacetimes, integrable systems and the KdV/mKdV hierarchies, JHEP 08 (2019) 079 [arXiv:1906.11226] [INSPIRE].
M. Cárdenas, F. Correa, K. Lara and M. Pino, Integrable Systems and Spacetime Dynamics, Phys. Rev. Lett. 127 (2021) 161601 [arXiv:2104.09676] [INSPIRE].
A. Achúcarro and P.K. Townsend, Extended Supergravities in d = (2 + 1) as Chern-Simons Theories, Phys. Lett. B 229 (1989) 383 [INSPIRE].
P.S. Howe, J.M. Izquierdo, G. Papadopoulos and P.K. Townsend, New supergravities with central charges and Killing spinors in (2 + 1)-dimensions, Nucl. Phys. B 467 (1996) 183 [hep-th/9505032] [INSPIRE].
M. Bañados, R. Troncoso and J. Zanelli, Higher dimensional Chern-Simons supergravity, Phys. Rev. D 54 (1996) 2605 [gr-qc/9601003] [INSPIRE].
M. Henneaux, L. Maoz and A. Schwimmer, Asymptotic dynamics and asymptotic symmetries of three-dimensional extended AdS supergravity, Annals Phys. 282 (2000) 31 [hep-th/9910013] [INSPIRE].
A. Giacomini, R. Troncoso and S. Willison, Three-dimensional supergravity reloaded, Class. Quant. Grav. 24 (2007) 2845 [hep-th/0610077] [INSPIRE].
G. Barnich, L. Donnay, J. Matulich and R. Troncoso, Asymptotic symmetries and dynamics of three-dimensional flat supergravity, JHEP 08 (2014) 071 [arXiv:1407.4275] [INSPIRE].
G. Barnich, L. Donnay, J. Matulich and R. Troncoso, Super-BMS3 invariant boundary theory from three-dimensional flat supergravity, JHEP 01 (2017) 029 [arXiv:1510.08824] [INSPIRE].
O. Fuentealba, J. Matulich and R. Troncoso, Asymptotic structure of 𝒩 = 2 supergravity in 3D: extended super-BMS3 and nonlinear energy bounds, JHEP 09 (2017) 030 [arXiv:1706.07542] [INSPIRE].
R. Caroca, P. Concha, O. Fierro and E. Rodríguez, Three-dimensional Poincaré supergravity and N -extended supersymmetric BMS3 algebra, Phys. Lett. B 792 (2019) 93 [arXiv:1812.05065] [INSPIRE].
N. Banerjee, A. Bhattacharjee, Neetu and T. Neogi, New 𝒩 = 2 SuperBMS3 algebra and invariant dual theory for 3D supergravity, JHEP 11 (2019) 122 [arXiv:1905.10239] [INSPIRE].
R. Caroca, P. Concha, O. Fierro and E. Rodríguez, On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions, Eur. Phys. J. C 80 (2020) 29 [arXiv:1908.09150] [INSPIRE].
N. Banerjee, A. Bhattacharjee, S. Biswas and T. Neogi, Dual theory for maximally 𝒩 extended flat supergravity, JHEP 05 (2022) 179 [arXiv:2110.05919] [INSPIRE].
M.P. Blencowe, A Consistent Interacting Massless Higher Spin Field Theory in D = (2 + 1), Class. Quant. Grav. 6 (1989) 443 [INSPIRE].
E. Bergshoeff, M.P. Blencowe and K.S. Stelle, Area Preserving Diffeomorphisms and Higher Spin Algebra, Commun. Math. Phys. 128 (1990) 213 [INSPIRE].
M. Henneaux and S.-J. Rey, Nonlinear W∞ as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [INSPIRE].
M. Gutperle and P. Kraus, Higher Spin Black Holes, JHEP 05 (2011) 022 [arXiv:1103.4304] [INSPIRE].
M. Ammon, M. Gutperle, P. Kraus and E. Perlmutter, Spacetime Geometry in Higher Spin Gravity, JHEP 10 (2011) 053 [arXiv:1106.4788] [INSPIRE].
A. Castro, E. Hijano, A. Lepage-Jutier and A. Maloney, Black Holes and Singularity Resolution in Higher Spin Gravity, JHEP 01 (2012) 031 [arXiv:1110.4117] [INSPIRE].
M. Henneaux, G. Lucena Gómez, J. Park and S.-J. Rey, Super- W(infinity) Asymptotic Symmetry of Higher-Spin AdS3 Supergravity, JHEP 06 (2012) 037 [arXiv:1203.5152] [INSPIRE].
A. Pérez, D. Tempo and R. Troncoso, Higher spin gravity in 3D: Black holes, global charges and thermodynamics, Phys. Lett. B 726 (2013) 444 [arXiv:1207.2844] [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Towards metric-like higher-spin gauge theories in three dimensions, J. Phys. A 46 (2013) 214017 [arXiv:1208.1851] [INSPIRE].
A. Pérez, D. Tempo and R. Troncoso, Higher spin black hole entropy in three dimensions, JHEP 04 (2013) 143 [arXiv:1301.0847] [INSPIRE].
M. Henneaux, A. Pérez, D. Tempo and R. Troncoso, Chemical potentials in three-dimensional higher spin anti-de Sitter gravity, JHEP 12 (2013) 048 [arXiv:1309.4362] [INSPIRE].
C. Bunster, M. Henneaux, A. Pérez, D. Tempo and R. Troncoso, Generalized Black Holes in Three-dimensional Spacetime, JHEP 05 (2014) 031 [arXiv:1404.3305] [INSPIRE].
Y.M. Zinoviev, Hypergravity in AdS3, Phys. Lett. B 739 (2014) 106 [arXiv:1408.2912] [INSPIRE].
O. Fuentealba, J. Matulich and R. Troncoso, Extension of the Poincaré group with half-integer spin generators: hypergravity and beyond, JHEP 09 (2015) 003 [arXiv:1505.06173] [INSPIRE].
O. Fuentealba, J. Matulich and R. Troncoso, Asymptotically flat structure of hypergravity in three spacetime dimensions, JHEP 10 (2015) 009 [arXiv:1508.04663] [INSPIRE].
M. Henneaux, A. Pérez, D. Tempo and R. Troncoso, Extended anti-de Sitter Hypergravity in 2 + 1 Dimensions and Hypersymmetry Bounds, in International Workshop on Higher Spin Gauge Theories, Singapore (2015), pg. 139 [arXiv:1512.08603] [INSPIRE].
D. Grumiller, A. Pérez, S. Prohazka, D. Tempo and R. Troncoso, Higher Spin Black Holes with Soft Hair, JHEP 10 (2016) 119 [arXiv:1607.05360] [INSPIRE].
D. Grumiller, W. Merbis and M. Riegler, Most general flat space boundary conditions in three-dimensional Einstein gravity, Class. Quant. Grav. 34 (2017) 184001 [arXiv:1704.07419] [INSPIRE].
L. Ravera, AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit, Phys. Lett. B 795 (2019) 331 [arXiv:1905.00766] [INSPIRE].
L. Avilés, J. Gomis and D. Hidalgo, Stringy (Galilei) Newton-Hooke Chern-Simons Gravities, JHEP 09 (2019) 015 [arXiv:1905.13091] [INSPIRE].
F. Ali and L. Ravera, 𝒩-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions, JHEP 02 (2020) 128 [arXiv:1912.04172] [INSPIRE].
P. Concha, M. Ipinza, L. Ravera and E. Rodríguez, Non-relativistic three-dimensional supergravity theories and semigroup expansion method, JHEP 02 (2021) 094 [arXiv:2010.01216] [INSPIRE].
P. Concha, L. Ravera and E. Rodríguez, Three-dimensional non-relativistic supergravity and torsion, Eur. Phys. J. C 82 (2022) 220 [arXiv:2112.05902] [INSPIRE].
R. Caroca, D.M. Peñafiel and P. Salgado-Rebolledo, Non-relativistic spin-3 symmetries in 2 + 1 dimensions from expanded/extended Nappi-Witten algebras, arXiv:2208.00602 [INSPIRE].
M. Henneaux, C. Martínez, R. Troncoso and J. Zanelli, Black holes and asymptotics of 2 + 1 gravity coupled to a scalar field, Phys. Rev. D 65 (2002) 104007 [hep-th/0201170] [INSPIRE].
J.D. Brown and M. Henneaux, Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity, Commun. Math. Phys. 104 (1986) 207 [INSPIRE].
J. de Boer and J.I. Jottar, Thermodynamics of higher spin black holes in AdS3, JHEP 01 (2014) 023 [arXiv:1302.0816] [INSPIRE].
G. Barnich, Conserved charges in gravitational theories: Contribution from scalar fields, Ann. U. Craiova Phys. 12 (2002) 14 [gr-qc/0211031] [INSPIRE].
G. Clément, Black hole mass and angular momentum in 2 + 1 gravity, Phys. Rev. D 68 (2003) 024032 [gr-qc/0301129] [INSPIRE].
J. Gegenberg, C. Martínez and R. Troncoso, A Finite action for three-dimensional gravity with a minimally coupled scalar field, Phys. Rev. D 67 (2003) 084007 [hep-th/0301190] [INSPIRE].
M.-I. Park, Fate of three-dimensional black holes coupled to a scalar field and the Bekenstein-Hawking entropy, Phys. Lett. B 597 (2004) 237 [hep-th/0403089] [INSPIRE].
M. Bañados and S. Theisen, Scale invariant hairy black holes, Phys. Rev. D 72 (2005) 064019 [hep-th/0506025] [INSPIRE].
Y.S. Myung, Phase transition for black holes with scalar hair and topological black holes, Phys. Lett. B 663 (2008) 111 [arXiv:0801.2434] [INSPIRE].
F. Correa, C. Martínez and R. Troncoso, Scalar solitons and the microscopic entropy of hairy black holes in three dimensions, JHEP 01 (2011) 034 [arXiv:1010.1259] [INSPIRE].
N. Lashkari, Holographic Symmetry-Breaking Phases in AdS3/CFT2, JHEP 11 (2011) 104 [arXiv:1011.3520] [INSPIRE].
F. Correa, C. Martínez and R. Troncoso, Hairy Black Hole Entropy and the Role of Solitons in Three Dimensions, JHEP 02 (2012) 136 [arXiv:1112.6198] [INSPIRE].
S. Hyun, J. Jeong and S.-H. Yi, Fake Supersymmetry and Extremal Black Holes, JHEP 03 (2013) 042 [arXiv:1210.6273] [INSPIRE].
J. Aparício, D. Grumiller, E. Lopez, I. Papadimitriou and S. Stricker, Bootstrapping gravity solutions, JHEP 05 (2013) 128 [arXiv:1212.3609] [INSPIRE].
W. Xu, J. Wang and X.-h. Meng, A Note on Entropy Relations of Black Hole Horizons, Int. J. Mod. Phys. A 29 (2014) 1450088 [arXiv:1401.5180] [INSPIRE].
W. Xu, Exact black hole formation in three dimensions, Phys. Lett. B 738 (2014) 472 [arXiv:1409.3368] [INSPIRE].
B. Ahn, S. Hyun, S.-A. Park and S.-H. Yi, Scaling symmetry and scalar hairy rotating AdS3 black holes, Phys. Rev. D 93 (2016) 024041 [arXiv:1508.06484] [INSPIRE].
L. Avilés, H. Maeda and C. Martínez, Exact black-hole formation with a conformally coupled scalar field in three dimensions, Class. Quant. Grav. 35 (2018) 245001 [arXiv:1808.10040] [INSPIRE].
F. Correa, A. Faúndez and C. Martínez, Rotating hairy black hole and its microscopic entropy in three spacetime dimensions, Phys. Rev. D 87 (2013) 027502 [arXiv:1211.4878] [INSPIRE].
T. Regge and C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Annals Phys. 88 (1974) 286 [INSPIRE].
J. Matulich, A. Pérez, D. Tempo and R. Troncoso, Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics, JHEP 05 (2015) 025 [arXiv:1412.1464] [INSPIRE].
M. Bañados, C. Teitelboim and J. Zanelli, The Black hole in three-dimensional space-time, Phys. Rev. Lett. 69 (1992) 1849 [hep-th/9204099] [INSPIRE].
M. Bañados, M. Henneaux, C. Teitelboim and J. Zanelli, Geometry of the (2 + 1) black hole, Phys. Rev. D 48 (1993) 1506 [Erratum ibid. 88 (2013) 069902] [gr-qc/9302012] [INSPIRE].
S. Carlip and C. Teitelboim, Aspects of black hole quantum mechanics and thermodynamics in (2 + 1)-dimensions, Phys. Rev. D 51 (1995) 622 [gr-qc/9405070] [INSPIRE].
J.M. Maldacena and A. Strominger, AdS3 black holes and a stringy exclusion principle, JHEP 12 (1998) 005 [hep-th/9804085] [INSPIRE].
J. Oliva, D. Tempo and R. Troncoso, Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity, JHEP 07 (2009) 011 [arXiv:0905.1545] [INSPIRE].
E. Ayón-Beato, A. Garbarz, G. Giribet and M. Hassaïne, Lifshitz Black Hole in Three Dimensions, Phys. Rev. D 80 (2009) 104029 [arXiv:0909.1347] [INSPIRE].
A. Pérez, D. Tempo and R. Troncoso, Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity, JHEP 07 (2011) 093 [arXiv:1106.4849] [INSPIRE].
H.A. Gonzalez, D. Tempo and R. Troncoso, Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes, JHEP 11 (2011) 066 [arXiv:1107.3647] [INSPIRE].
E.A. Bergshoeff, O. Hohm and P.K. Townsend, Massive Gravity in Three Dimensions, Phys. Rev. Lett. 102 (2009) 201301 [arXiv:0901.1766] [INSPIRE].
R. Troncoso and M. Tsoukalas, Conformally coupled scalar fields in higher dimensions and a generalization of the Yamabe problem, Preprint CECS-PHY-11/11.
C. Martínez and J. Zanelli, Conformally dressed black hole in (2 + 1)-dimensions, Phys. Rev. D 54 (1996) 3830 [gr-qc/9604021] [INSPIRE].
M. Visser, Dirty black holes: Entropy as a surface term, Phys. Rev. D 48 (1993) 5697 [hep-th/9307194] [INSPIRE].
A. Ashtekar, A. Corichi and D. Sudarsky, Nonminimally coupled scalar fields and isolated horizons, Class. Quant. Grav. 20 (2003) 3413 [gr-qc/0305044] [INSPIRE].
M. Hortacsu, H.T. Ozcelik and B. Yapiskan, Properties of solutions in (2 + 1)-dimensions, Gen. Rel. Grav. 35 (2003) 1209 [gr-qc/0302005] [INSPIRE].
K. Hotta, Y. Hyakutake, T. Kubota, T. Nishinaka and H. Tanida, The CFT-interpolating Black Hole in Three Dimensions, JHEP 01 (2009) 010 [arXiv:0811.0910] [INSPIRE].
Y. Kwon, S. Nam, J.-D. Park and S.-H. Yi, Extremal Black Holes and Holographic C-Theorem, Nucl. Phys. B 869 (2013) 189 [arXiv:1208.4509] [INSPIRE].
W. Xu and L. Zhao, Charged black hole with a scalar hair in (2 + 1) dimensions, Phys. Rev. D 87 (2013) 124008 [arXiv:1305.5446] [INSPIRE].
L. Zhao, W. Xu and B. Zhu, Novel rotating hairy black hole in (2 + 1)-dimensions, Commun. Theor. Phys. 61 (2014) 475 [arXiv:1305.6001] [INSPIRE].
J. Naji, Energy Loss of a Heavy Particle near 3D Charged Rotating Hairy Black Hole, Eur. Phys. J. C 74 (2014) 2697 [arXiv:1401.4422] [INSPIRE].
S.H. Mazharimousavi and M. Halilsoy, Einstein-Born-Infeld black holes with a scalar hair in three dimensions, Mod. Phys. Lett. A 30 (2015) 1550177 [arXiv:1405.2956] [INSPIRE].
W. Xu, L. Zhao and D.-C. Zou, Three dimensional rotating hairy black holes, asymptotics and thermodynamics, arXiv:1406.7153 [INSPIRE].
M. Cárdenas, O. Fuentealba and C. Martínez, Three-dimensional black holes with conformally coupled scalar and gauge fields, Phys. Rev. D 90 (2014) 124072 [arXiv:1408.1401] [INSPIRE].
W. Xu and D.-C. Zou, (2 + 1) -Dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory, Gen. Rel. Grav. 49 (2017) 73 [arXiv:1408.1998] [INSPIRE].
P.A. González, J. Saavedra and Y. Vásquez, Three-Dimensional Hairy Black Holes in Teleparallel Gravity, Astrophys. Space Sci. 357 (2015) 143 [arXiv:1411.2193] [INSPIRE].
J. Naji and S. Heshmatian, Novel Rotating Hairy Black Hole in (2 + 1)-Dimensions and Shear Viscosity to Entropy Ratio, Int. J. Theor. Phys. 53 (2014) 2579 [INSPIRE].
E. Ayón-Beato, M. Bravo-Gaete, F. Correa, M. Hassaïne, M.M. Juárez-Aubry and J. Oliva, First law and anisotropic Cardy formula for three-dimensional Lifshitz black holes, Phys. Rev. D 91 (2015) 064006 [Addendum ibid. 96 (2017) 049903] [arXiv:1501.01244] [INSPIRE].
Q. Wen, Strategy to Construct Exact Solutions in Einstein-Scalar Gravities, Phys. Rev. D 92 (2015) 104002 [arXiv:1501.02829] [INSPIRE].
E. Ayón-Beato, M. Hassaïne and J.A. Méndez-Zavaleta, (Super-)renormalizably dressed black holes, Phys. Rev. D 92 (2015) 024048 [Addendum ibid. 96 (2017) 049905] [arXiv:1506.02277] [INSPIRE].
Z.-Y. Fan and B. Chen, Exact formation of hairy planar black holes, Phys. Rev. D 93 (2016) 084013 [arXiv:1512.09145] [INSPIRE].
B. Harms and A. Stern, Spinning σ-model solitons in 2 + 1 anti-de Sitter space, Phys. Lett. B 763 (2016) 401 [arXiv:1608.05116] [INSPIRE].
H.T. Özçelik, R. Kaya and M. Hortaçsu, Einstein gravity with torsion induced by the scalar field, Annals Phys. 393 (2018) 132 [arXiv:1611.07496] [INSPIRE].
B. Harms and A. Stern, Growing Hair on the extremal BTZ black hole, Phys. Lett. B 769 (2017) 465 [arXiv:1703.10234] [INSPIRE].
C. Erices and C. Martínez, Rotating hairy black holes in arbitrary dimensions, Phys. Rev. D 97 (2018) 024034 [arXiv:1707.03483] [INSPIRE].
Z.-Y. Tang, Y.C. Ong, B. Wang and E. Papantonopoulos, General black hole solutions in (2 + 1)-dimensions with a scalar field nonminimally coupled to gravity, Phys. Rev. D 100 (2019) 024003 [arXiv:1901.07310] [INSPIRE].
T. Karakasis, E. Papantonopoulos, Z.-Y. Tang and B. Wang, Black holes of (2 + 1)-dimensional f (R) gravity coupled to a scalar field, Phys. Rev. D 103 (2021) 064063 [arXiv:2101.06410] [INSPIRE].
P. Bueno, P.A. Cano, J. Moreno and G. van der Velde, Regular black holes in three dimensions, Phys. Rev. D 104 (2021) L021501 [arXiv:2104.10172] [INSPIRE].
T. Karakasis, E. Papantonopoulos, Z.-Y. Tang and B. Wang, (2 + 1)-dimensional black holes in f (R, ϕ) gravity, Phys. Rev. D 105 (2022) 044038 [arXiv:2201.00035] [INSPIRE].
P.J. Arias, P. Bargueño, E. Contreras and E. Fuenmayor, 2 + 1 Einstein-Klein-Gordon black holes by gravitational decoupling, Astronomy 1 (2022) 2 [arXiv:2203.00661] [INSPIRE].
C. Desa, W. Ccuiro and D. Choque, Exact hairy black holes asymptotically AdS2+1, arXiv:2210.06421 [INSPIRE].
T. Karakasis, E. Papantonopoulos, Z.-Y. Tang and B. Wang, Rotating (2 + 1)-dimensional Black Holes in Einstein-Maxwell-Dilaton Theory, arXiv:2210.15704 [INSPIRE].
P. Bueno, P.A. Cano, J. Moreno and G. van der Velde, Electromagnetic Generalized Quasi-topological gravities in (2 + 1) dimensions, arXiv:2212.00637 [INSPIRE].
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Cárdenas, M., Fuentealba, O., Martínez, C. et al. Gravity coupled to a scalar field from a Chern-Simons action: describing rotating hairy black holes and solitons with gauge fields. J. High Energ. Phys. 2023, 58 (2023). https://doi.org/10.1007/JHEP02(2023)058
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DOI: https://doi.org/10.1007/JHEP02(2023)058