The D-dimensional charged AdS black holes solutions in polytropic dark energy from Barrow entropy

Abstract This paper mainly aims to solve the anti-deSitter Black Holes (AdS BH) under the Barrow entropy under polytropic gas fluid, especially the Chaplygin gas. First, we develop this last polytropic model in detail to then obtain the possible solutions and thermodynamic conditions on the energy momentum and the Barrow entropy for spacetimes of spatial dimension $$D&gt;3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . Then, we focus on thermodynamic solutions and the different impacts on the Barrow entropy of the black hole, the temperature profile, the mass, and the various physical quantities involved. Afterwards, we focus on the specific cases of the solutions of dimensions $$D=4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> and 5 to concretely test the models, especially from the point of view of the thermodynamic topology. Finally, we generalize everything by elaborating and testing the stability of the models to arrive at the thermal geometry of the AdS BH.

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