Abstract
In this paper, we investigate the phase structure of the black holes with one single higher spin hair, focusing specifically on the spin 3 and spin \( \widetilde{4} \) black holes. Based on dimensional analysis and the requirement of thermodynamic consistency, we derive a universal formula relating the entropy with the conserved charges for arbitrary AdS 3 higher spin black holes. Then we use it to study the phase structure of the higher spin black holes. We find that there are six branches of solutions in the spin 3 gravity, eight branches of solutions in the spin \( \widetilde{4} \) gravity and twelve branches of solutions in the G 2 gravity. In each case, all the branches are related by a simple angle shift in the entropy functions. In the spin 3 case, we reproduce all the results found before. In the spin \( \widetilde{4} \) case, we find that at low temperature it lies in the BTZ branch while at high temperature it undergoes a phase transition to one of the two other branches, depending on the signature of the chemical potential, a reflection of charge conjugate asymmetry found before.
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ArXiv ePrint: 1212.6593
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Chen, B., Long, J. & Wang, YN. Phase structure of higher spin black hole. J. High Energ. Phys. 2013, 17 (2013). https://doi.org/10.1007/JHEP03(2013)017
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DOI: https://doi.org/10.1007/JHEP03(2013)017