Thermodynamic stability and P–V criticality of nonsingular-AdS black holes endowed with clouds of strings
Abstract
Abstract We investigate the extended phase space thermodynamics of nonsingular-AdS black holes minimally coupled to clouds of strings in which we consider the cosmological constant ( $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> ) as the pressure ( P ) of the black holes and its conjugate variable thermodynamical volume ( V ) of the black holes. Owing to the background clouds of strings parameter ( a ), we analyse the Hawking temperature, entropy and specific heat on horizon radius for fixed-parameter k . We find that the strings clouds background does not alter small/large black hole (SBH/LBH) phase transition but occurs at a larger horizon radius, and two second-order phase transitions occur at a smaller horizon radius. Indeed, the G – T plots exhibit a swallowtail below the critical pressure, implying that the first-order phase transition is analogous to the liquid–gas phase transition at a lower temperature and lower critical pressure. To further examine the analogy between nonsingular-AdS black holes and a liquid–gas system, we derive the exact critical points and probe the effects of a cloud of strings on $$P-V$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mo>-</mml:mo> <mml:mi>V</mml:mi> </mml:mrow> </mml:math> criticality to find that the isotherms undergo liquid–gas like phase transition for $${\tilde{T}}\,<\,{\tilde{T}}_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mspace/> <mml:mo><</mml:mo> <mml:mspace/> <mml:msub> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> at lower $${\tilde{T}}_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mi>c</mml:mi> </mml:msub> </mml:math> . We have also calculated the critical exponents identical with Van der Walls fluid, i.e., same as those obtained before for arbitrary other AdS black holes, which implies that the background clouds of strings do not change the critical exponents.