Eur. Phys. J. Plus (2024) 139: 439
https://doi.org/10.1140/epjp/s13360-024-05235-7

Regular Article

Extended phase space thermodynamics of Bardeen–Letelier black holes in 4D Einstein–Gauss–Bonnet gravity

¹ Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology, 310023, Hangzhou, China
² Department of Mathematical Sciences, University of Zululand, Private Bag X1001, 3886, Kwa-Dlangezwa, South Africa
³ Centre for Theoretical Physics, Jamia Millia Islamia, 110025, New Delhi, India
⁴ Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X54001, 4000, Durban, South Africa
⁵ Department of Mathematical Sciences, University of Zululand, Private Bag X1001, 3886, Kwa-Dlangezwa, South Africa
⁶ Faculty of Natural Sciences, Mangosuthu University of Technology, P.O. Box 12363, 4026, Jacobs, South Africa

^a arunbidhan@gmail.com

Received: 8 February 2024
Accepted: 30 April 2024
Published online: 24 May 2024

Abstract

We use the black hole chemistry prescription, $P=-\mathrm{\Lambda }/8\pi$, to investigate the thermodynamic behavior of Bardeen-AdS black holes surrounded by clouds of strings in 4D EGB gravity. The Hawking temperature shows local maxima and minima at critical horizon radii $x_{\text{c}1}$ and $x_{\text{c}2}$, when we take $a<a_{\text{c}}$, signifying the existence of phase transition. Further, when we take the value of pressure less than critical pressure, the isobars on $\tilde{G}$–$\tilde{T}$ plane exhibit a swallowtail-like structure confirming the first-order phase transition between small and large stable black holes, but because of clouds of strings, it occurs at a lower temperature and lower critical pressure. In the limit $\tilde{\alpha }\to 0$, surrounded by a cloud of strings ($a\ne 0$) and with nonlinear electrodynamics (NED) switched off ($\tilde{g}=0$), the Hawking–Page phase transition exists, but it would be disappeared, and SBH/LBH phase transition recovers as soon one switch on the NED ($\tilde{g}\ne 0$). The effects of clouds of strings on P–V criticality suggest that the isotherms undergo liquid–gas-like phase transition for $\tilde{T}<{\tilde{T}}_{\text{c}}$ at lower ${\tilde{T}}_{\text{c}}$ and that the critical exponents identical with van der Walls fluid.