TY - JOUR

T1 - AdS monopole black hole and phase transition

AU - Miyashita, Shoichiro

AU - Maeda, Kei Ichi

N1 - Funding Information:
S.M. would like to thank Y. Hoshino and T. Kitamura for the useful discussions. This work was supported, in part, by grants-in-aid from the Scientific Research Fund of the Japan Society for the Promotion of Science (Grants No.25400276 and No.16K05362).
Publisher Copyright:
© 2016 American Physical Society.

PY - 2016/12/23

Y1 - 2016/12/23

N2 - We study the Einstein-SO(3)Yang-Mills-Higgs system with a negative cosmological constant and find the monopole black hole solutions as well as the trivial Reissner-Nordström black hole. We discuss thermodynamical stability of the monopole black hole in an isolated system. We expect a phase transition between those two black holes when the mass of a black hole increases or decreases. The type of phase transition depends on the cosmological constant Λ, as well as the vacuum expectation value v and the coupling constant λ of the Higgs field. Keeping λ small, we find there are two critical values of the cosmological constant, Λcr(1)(v) and Λcr(2)(v), which depend on v. If Λcr(1)(v)<Λ(<0), we find the first order transition, whereas if Λcr(2)(v)<Λ<Λcr(1)(v), the transition becomes second order. For the case of Λb(v)<Λ<Λ(2)(v), we again find the first order irreversible transition from the monopole black hole to the extreme Reissner-Nordström black hole. Beyond Λb(v), no monopole black hole exists. We also discuss thermodynamical properties of the monopole black hole in a thermal bath system.

AB - We study the Einstein-SO(3)Yang-Mills-Higgs system with a negative cosmological constant and find the monopole black hole solutions as well as the trivial Reissner-Nordström black hole. We discuss thermodynamical stability of the monopole black hole in an isolated system. We expect a phase transition between those two black holes when the mass of a black hole increases or decreases. The type of phase transition depends on the cosmological constant Λ, as well as the vacuum expectation value v and the coupling constant λ of the Higgs field. Keeping λ small, we find there are two critical values of the cosmological constant, Λcr(1)(v) and Λcr(2)(v), which depend on v. If Λcr(1)(v)<Λ(<0), we find the first order transition, whereas if Λcr(2)(v)<Λ<Λcr(1)(v), the transition becomes second order. For the case of Λb(v)<Λ<Λ(2)(v), we again find the first order irreversible transition from the monopole black hole to the extreme Reissner-Nordström black hole. Beyond Λb(v), no monopole black hole exists. We also discuss thermodynamical properties of the monopole black hole in a thermal bath system.

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U2 - 10.1103/PhysRevD.94.124037

DO - 10.1103/PhysRevD.94.124037

M3 - Article

AN - SCOPUS:85021944508

SN - 2470-0010

VL - 94

JO - Physical Review D

JF - Physical Review D

IS - 12

M1 - 124037

ER -