TY - JOUR

T1 - Gravity coupled to a scalar field from a Chern-Simons action

T2 - describing rotating hairy black holes and solitons with gauge fields

AU - Cárdenas, Marcela

AU - Fuentealba, Oscar

AU - Martínez, Cristián

AU - Troncoso, Ricardo

N1 - Publisher Copyright:
© 2023, The Author(s).

PY - 2023/2

Y1 - 2023/2

N2 - 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.

AB - 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.

KW - AdS-CFT Correspondence

KW - Black Holes

KW - Classical Theories of Gravity

UR - http://www.scopus.com/inward/record.url?scp=85148526992&partnerID=8YFLogxK

U2 - 10.1007/JHEP02(2023)058

DO - 10.1007/JHEP02(2023)058

M3 - Article

AN - SCOPUS:85148526992

SN - 1029-8479

VL - 2023

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 2

M1 - 58

ER -