Thermodynamical analysis with extended phase transition of AdS hairy black hole in gravitational decoupling theory

Abstract This article explores various thermodynamical aspects and the extended phase space of the AdS hairy black hole within the context of gravitational decoupling. This study focused on thermodynamic properties such as geometrical mass, Hawking temperature, entropy, specific heat, Gibbs free energy (both locally and globally) and P-V criticality at the horizon radius. The thermodynamic stability of the AdS hairy black hole has been established based on its positive heat capacity. The analysis of Gibbs free energy is utilized to investigate the behavior of the first-order phase transition. Thermodynamic pressure, denoted by P , is related to the cosmological constant by the formula <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:mo>−</mml:mo> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mrow> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>8</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:mfrac> </mml:mstyle> </mml:math> . In addition, a numerical investigation has been carried out to examine the equation of the state parameter and its critical values.

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