https://doi.org/10.1140/epjc/s10052-018-5652-0
Regular Article - Theoretical Physics
On the thermodynamics of the black hole and hairy black hole transitions in the asymptotically flat spacetime with a box
1
School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China
2
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou, 225009, China
3
Department of Physics and Astronomy, Center of Astronomy and Astrophysics, Shanghai Jiao Tong University, Shanghai, 200240, China
4
School of Physics, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China
* e-mail: yanpengphy@163.com
Received:
24
October
2017
Accepted:
14
February
2018
Published online:
2
March
2018
We study the asymptotically flat quasi-local black hole/hairy black hole model with nonzero mass of the scalar field. We disclose effects of the scalar mass on transitions in a grand canonical ensemble with condensation behaviors of the parameter 
, which is similar to approaches in holographic theories. We find that a more negative scalar mass makes the phase transition easier. We also obtain the analytical relation 
around the critical phase transition points, implying a second order phase transition. Besides the parameter , we show that metric solutions can be used to disclose properties of the transitions. In this work, we observe that phase transitions in a box are strikingly similar to holographic transitions in AdS gravity and the similarity provides insights into holographic theories.
© The Author(s), 2018
