Thermodynamic geometry of 5D <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math>-charged black holes in extended thermodynamic space

Abstract

We study a five-dimensional $R$-charged black hole in extended thermodynamic space. Here, we consider pressure and volume as conjugate thermodynamic variables. We begin with a thermodynamic study based on Maxwell's equal area rule and then compute the Ruppeiner scalar curvature for a number of different charge combinations. We mainly focus on three characteristic cases: an $R$-charged black hole with three equal charges, two equal charges, and three unequal charges. Based on our analysis, we make an attempt to relate the Ruppeiner scalar curvature with the phase structure of the black hole.