Eur. Phys. J. Plus (2019) 134: 110
https://doi.org/10.1140/epjp/i2019-12514-5

Regular Article

The last lost charge and phase transition in Schwarzschild AdS minimally coupled to a cloud of strings

Faculty of Physics, Semnan University, P.C. 35131-19111, Semnan, Iran

^* e-mail: hghafarnejad@semnan.ac.ir

Received: 11 December 2018
Accepted: 8 January 2019
Published online: 19 March 2019

Abstract

In this paper we study the Schwarzschild AdS black hole with a cloud of string background in an extended phase space and investigate a new phase transition related to the topological charge. By treating the topological charge as a new charge for the black hole solution we study its thermodynamics in this new extended phase space. We treat by two approaches to study the phase transition behavior via both T-S and P-v criticality and we find the results confirm each other in a nice way. It is shown that a cloud of strings affects the critical physical quantities and it could be observed an interesting Van der Waals-like phase transition in the extended thermodynamics. The swallow tail-like behavior is also observed in the free energy-temperature diagram. We observe in the limit that the small/large black hole phase transition reduces to the Hawking-Page phase transition as we expected. We can deduce that the impact of the cloud of strings in the Schwarzschild black hole can bring a Van der Waals-like black hole phase transition.