A new approach toward geometrical concept of black hole thermodynamics

The European Physical Journal C

Behzad Eslam Panah¹  Shahram Panahiyan¹  Mehrab Momennia¹  Seyed Hossein Hendi² 

[1] Physics Department and Biruni Observatory, College of Sciences, Shiraz University, 71454, Shiraz, Iran;Physics Department and Biruni Observatory, College of Sciences, Shiraz University, 71454, Shiraz, Iran;Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha, Iran;

关键词: Black Hole;    Heat Capacity;    Black Hole Solution;    Divergence Point;    Ricci Scalar;   

DOI  :  10.1140/epjc/s10052-015-3701-5

来源: Springer

【 摘 要 】

Motivated by the energy representation of Riemannian metric, in this paper we study different approaches toward the geometrical concept of black hole thermodynamics. We investigate thermodynamical Ricci scalar of Weinhold, Ruppeiner and Quevedo metrics and show that their number and location of divergences do not coincide with phase transition points arisen from heat capacity. Next, we introduce a new metric to solve these problems. We show that the denominator of the Ricci scalar of the new metric contains terms which coincide with different types of phase transitions. We elaborate the effectiveness of the new metric and shortcomings of the previous metrics with some examples. Furthermore, we find a characteristic behavior of the new thermodynamical Ricci scalar which enables one to distinguish two types of phase transitions. In addition, we generalize the new metric for the cases of more than two extensive parameters and show that in these cases the divergencies of thermodynamical Ricci scalar coincide with phase transition points of the heat capacity.

【 授权许可】

CC BY