Topological charges via Barrow entropy of black hole in metric-affine gravity

Abstract This paper examines distinct ensembles such as canonical, mixed, and grand canonical ensembles of recently postulated black hole which is considered to be an ideal solution of metric-affine gravity utilizing the Duan’s $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> -mapping theory. In the scenario, charged and uncharged topological characteristics associated to thermodynamic stability criteria are explored. In contrast to the canonical ensemble, which is always possesses the constant electric and magnetic charges, but mixed ensemble possesses the constant potentials (both magnetic and electric). Also, grand canonical ensemble maintains the constant electric and magnetic potentials for both charges. Initially, we find the topological classes connected via critical points in all of the aforementioned ensembles.