Abstract
This work deals with the applications of thermodynamical geometries on conformal gravity black holes (CGBH) consisting of conformal parameters a and k. The stability of black hole (BH) addressed with the aid of small, middle, large and divergency roots, respectively. For this purpose, graphical behavior of heat capacity and temperature versus horizon radius is presented which help us to show the stability conditions. Further, studied the different geometries like Weinhold, Ruppeiner, Geometrothermodynamics (GTD) and Hendi-Panahiyah-Eslam-Momennia (HPEM), and found relationship between divergency of scalar curvature and zeros of heat capacity. As a result, it is noticed that Ruppeiner, HPEM and GTD metric exhibit more important information as compared to Weinhold.
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