Primary scalar hair in Gauss–Bonnet black holes with Thurston horizons

Abstract In this work, we construct novel asymptotically locally AdS $$_5$$ 5 black hole solutions of Einstein–Gauss–Bonnet theory at the Chern–Simons point, supported by a scalar field that generates a primary hair. The strength of the scalar field is governed by an independent integration constant...

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Main Authors: Luis Guajardo, Julio Oliva
Format: Article
Language:English
Published: SpringerOpen 2025-02-01
Series:European Physical Journal C: Particles and Fields
Online Access:https://doi.org/10.1140/epjc/s10052-025-13869-9
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author Luis Guajardo
Julio Oliva
author_facet Luis Guajardo
Julio Oliva
author_sort Luis Guajardo
collection DOAJ
description Abstract In this work, we construct novel asymptotically locally AdS $$_5$$ 5 black hole solutions of Einstein–Gauss–Bonnet theory at the Chern–Simons point, supported by a scalar field that generates a primary hair. The strength of the scalar field is governed by an independent integration constant; when this constant vanishes, the spacetime reduces to a black hole geometry devoid of hair. The existence of these solutions is intrinsically tied to the horizon metric, which is modeled by three non-trivial Thurston geometries: Nil, Solv, and $$SL(2,{\mathbb {R}}).$$ S L ( 2 , R ) . The quadratic part of the scalar field action corresponds to a conformally coupled scalar in five dimensions -an invariance of the matter sector that is explicitly broken by the introduction of a quartic self-interaction. These black holes are characterized by two distinct parameters: the horizon radius and the temperature. Notably, there exists a straight line in this parameter space along which the horizon geometry exhibits enhanced isometries, corresponding to solutions previously reported in JHEP 02, 014 (2014). Away from this line, for a fixed horizon radius and temperatures above or below a critical value, the metric’s isometries undergo spontaneous breaking. Employing the Regge–Teitelboim approach, we compute the mass and entropy of these solutions, both of which vanish. Despite this, only one of the integration constants can be interpreted as hair, as the other modifies the local geometry at the conformal boundary. Finally, for Solv horizon geometries, we extend these hairy solutions to six dimensions.
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spelling doaj-art-56cb078554e14b78b221f940c6db71e62025-02-09T12:51:54ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-02-018521810.1140/epjc/s10052-025-13869-9Primary scalar hair in Gauss–Bonnet black holes with Thurston horizonsLuis Guajardo0Julio Oliva1Instituto de Investigación Interdisciplinaria, Vicerrectoría Académica, Universidad de TalcaDepartamento de Física, Universidad de ConcepciónAbstract In this work, we construct novel asymptotically locally AdS $$_5$$ 5 black hole solutions of Einstein–Gauss–Bonnet theory at the Chern–Simons point, supported by a scalar field that generates a primary hair. The strength of the scalar field is governed by an independent integration constant; when this constant vanishes, the spacetime reduces to a black hole geometry devoid of hair. The existence of these solutions is intrinsically tied to the horizon metric, which is modeled by three non-trivial Thurston geometries: Nil, Solv, and $$SL(2,{\mathbb {R}}).$$ S L ( 2 , R ) . The quadratic part of the scalar field action corresponds to a conformally coupled scalar in five dimensions -an invariance of the matter sector that is explicitly broken by the introduction of a quartic self-interaction. These black holes are characterized by two distinct parameters: the horizon radius and the temperature. Notably, there exists a straight line in this parameter space along which the horizon geometry exhibits enhanced isometries, corresponding to solutions previously reported in JHEP 02, 014 (2014). Away from this line, for a fixed horizon radius and temperatures above or below a critical value, the metric’s isometries undergo spontaneous breaking. Employing the Regge–Teitelboim approach, we compute the mass and entropy of these solutions, both of which vanish. Despite this, only one of the integration constants can be interpreted as hair, as the other modifies the local geometry at the conformal boundary. Finally, for Solv horizon geometries, we extend these hairy solutions to six dimensions.https://doi.org/10.1140/epjc/s10052-025-13869-9
spellingShingle Luis Guajardo
Julio Oliva
Primary scalar hair in Gauss–Bonnet black holes with Thurston horizons
European Physical Journal C: Particles and Fields
title Primary scalar hair in Gauss–Bonnet black holes with Thurston horizons
title_full Primary scalar hair in Gauss–Bonnet black holes with Thurston horizons
title_fullStr Primary scalar hair in Gauss–Bonnet black holes with Thurston horizons
title_full_unstemmed Primary scalar hair in Gauss–Bonnet black holes with Thurston horizons
title_short Primary scalar hair in Gauss–Bonnet black holes with Thurston horizons
title_sort primary scalar hair in gauss bonnet black holes with thurston horizons
url https://doi.org/10.1140/epjc/s10052-025-13869-9
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AT juliooliva primaryscalarhairingaussbonnetblackholeswiththurstonhorizons