Thermodynamics of rotating black holes with scalar hair in three dimensions

Abstract

Introducing a new form of scalar potential V (φ), we derive a proper form of the rotating black hole solution in three-dimensional Einstein gravity with nonminimally coupled scalar field and find that the first law of thermodynamics of this new rotating hairy black hole can be protected, where the scalar field parameter B is constrained to relate to the black hole size. We also disclose the Hawking-Page phase transition between this rotating hairy black holes and the pure thermal radiation. Moreover, we study phase transitions between this rotating hairy black hole and rotating BTZ black hole. Considering the matchings for the temperature and angular momentum, we find that the rotating BTZ black hole always has smaller free energy which is a thermodynamically more preferred phase. Additionally, we evaluate the thermodynamics of the rotating black hole with minimally coupled scalar hair in three dimensions, which exhibits that the thermodynamical behaviors of this rotating hairy black hole are very similar to those of the rotating black hole with nonminimally coupled scalar hair.

A note on Maxwell’s equal area law for black hole phase transition

“…With this interpretation of the cosmological constant, many works on the AdS black hole phase transition were carried out [21][22][23][24][25][26][27][28][29]. In Ref.…”

Quantum tunneling from rotating black holes with scalar hair in three dimensions

“…That is, any test body dropped into the BH will circumnavigate the BH at this frequency as it approaches the event horizon. Furthermore, one can easily verify that the first law of thermodynamics [28] holds:…”

“…Without loss of generality, we assume that B is a positive real number. Meanwhile, it is worth noting that when B = 0 metric (1) describes the rotating BTZ BH [28].…”

“…On the other hand, since the seminal work of Deser et al [21][22][23] and Witten [24,25], the foundations of classical gravity and QG have increasingly been investigated by GR in 3D spacetime [26]. Therefore, we here consider a 3D RSHBH [19,[27][28][29][30] as a solution to the Einstein gravity equations with a non-minimally coupled scalar field φ. In the absence of the scalar field (φ = 0), the 3D RSHBH reduces to the well-known rotating Bañados-Teitelboim-Zanelli (BTZ) BH [31][32][33].…”

$$(2+1)$$ ( 2 + 1 ) -Dimensional charged black holes with scalar hair in Einstein–Power–Maxwell Theory

“…Furthermore, the charged [47], rotating [48][49][50][51], charged rotating [52] and Einstein-Born-Infeld [53] black holes with non-minimally scalar hair and rotating black hole dressed with minimal scalar field hair [54] in the (2 + 1) dimensional Einstein's gravity, and black hole dressed by a (non)minimally scalar field in New Massive Gravity [55] have been discussed. Beyond the linear Maxwell electromagnetism in theory with scalar fields, in this paper, we study the charged black hole solution with non-minimally coupled scalar field in the (2 + 1)-dimensional Einstein-Power-Maxwell (EPM) theory.…”