Thermodynamic Geometry and Topological Einstein-Yang-Mills Black Holes
  From the perspective of the statistical fluctuation theory, we explore the role of the thermodynamic geometries and vacuum (in)stability properties for the topological Einstein-Yang-Mills black holes. In this paper, from the perspective of the state-space surface and chemical Wienhold surface, we provide the criteria for the local and global statistical stability of an ensemble of topological Einstein-Yang-Mills black holes in arbitrary spacetime dimensions $D\ge 5$. Finally, as per the formulations of the thermodynamic geometry, we offer a parametric account of the statistical consequences in both the local and global fluctuation regimes of the topological Einstein-Yang-Mills black holes. 
Stefano Bellucci and Bhupendra Nath Tiwari
hep-th gr-qc