# Thermodynamic Metrics and Black Hole Physics

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## Abstract

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## 1. Introduction

## 2. Ruppeiner Geometry

## 3. Physical Interpretation and the Role of Curvature

## 4. Entropic Substances

## 5. The Transition to Black Holes

## 6. Kerr Black Holes

**Figure 1.**Contour curves of equal Hawking temperature T. The Hawking temperature vanishes at the edge of the wedge that corresponds to the outer horizon, is negative outside and diverges on the null cone.

**Figure 2.**Contour curves of equal Ruppeiner scalar curvature R. It is negative inside the wedge, positive outside and diverges both at the edge of the wedge and on the null cone.

**Figure 5.**Contour curves for entropy and mass (dashed). By moving inside the grey area, from near the edge of the wedge (large a) towards the center, one is able to decrease the mass (extract energy), even though the area of the event horizon (the entropy) increases [41], as it must according to Einstein’s theory.

## 7. The Kerr–Newman Family of Black Holes

## 8. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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Åman, J.E.; Bengtsson, I.; Pidokrajt, N.
Thermodynamic Metrics and Black Hole Physics. *Entropy* **2015**, *17*, 6503-6518.
https://doi.org/10.3390/e17096503

**AMA Style**

Åman JE, Bengtsson I, Pidokrajt N.
Thermodynamic Metrics and Black Hole Physics. *Entropy*. 2015; 17(9):6503-6518.
https://doi.org/10.3390/e17096503

**Chicago/Turabian Style**

Åman, Jan E., Ingemar Bengtsson, and Narit Pidokrajt.
2015. "Thermodynamic Metrics and Black Hole Physics" *Entropy* 17, no. 9: 6503-6518.
https://doi.org/10.3390/e17096503