| Summary: | Abstract A detailed discussion on phase transition, stability and microscopic structure of a charged black hole in anti-de Sitter (AdS) by using exponential entropy is presented. For this black hole, the thermodynamic characteristics such as the Hawking temperature, specific heat and the $$P-v$$ P - v curve will be developed and investigated with the variation of black hole horizon radius and monopole parameter. We also study the scalar curvatures of this black hole by using several thermodynamic geometry formulations, such as the Ruppeiner, Weinhold, HPEM, Quevedo in view of exponential entropy. Moreover, we extract the HPEM and Quevedo formulations of the charged AdS black hole which may provide more data on the phase-transition than the Weinhold and Ruppeiner techniques.
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