# Geometry of higher-dimensional black hole thermodynamics

## Abstract

We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d{>=}6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d{>=}5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta.

- Authors:

- Quantum and Field Theory group, Department of Physics, AlbaNova, Stockholm University, SE-106 91 Stockholm (Sweden)

- Publication Date:

- OSTI Identifier:
- 20795734

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.73.024017; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANGULAR MOMENTUM; BLACK HOLES; CONFIGURATION; COSMOLOGY; GEOMETRY; MANY-DIMENSIONAL CALCULATIONS; SPACE-TIME; THERMODYNAMICS

### Citation Formats

```
Aaman, Jan E., and Pidokrajt, Narit.
```*Geometry of higher-dimensional black hole thermodynamics*. United States: N. p., 2006.
Web. doi:10.1103/PHYSREVD.73.0.

```
Aaman, Jan E., & Pidokrajt, Narit.
```*Geometry of higher-dimensional black hole thermodynamics*. United States. doi:10.1103/PHYSREVD.73.0.

```
Aaman, Jan E., and Pidokrajt, Narit. Sun .
"Geometry of higher-dimensional black hole thermodynamics". United States.
doi:10.1103/PHYSREVD.73.0.
```

```
@article{osti_20795734,
```

title = {Geometry of higher-dimensional black hole thermodynamics},

author = {Aaman, Jan E. and Pidokrajt, Narit},

abstractNote = {We investigate thermodynamic curvatures of the Kerr and Reissner-Nordstroem (RN) black holes in spacetime dimensions higher than four. These black holes possess thermodynamic geometries similar to those in four-dimensional spacetime. The thermodynamic geometries are the Ruppeiner geometry and the conformally related Weinhold geometry. The Ruppeiner geometry for a d=5 Kerr black hole is curved and divergent in the extremal limit. For a d{>=}6 Kerr black hole there is no extremality but the Ruppeiner curvature diverges where one suspects that the black hole becomes unstable. The Weinhold geometry of the Kerr black hole in arbitrary dimension is a flat geometry. For the RN black hole the Ruppeiner geometry is flat in all spacetime dimensions, whereas its Weinhold geometry is curved. In d{>=}5 the Kerr black hole can possess more than one angular momentum. Finally we discuss the Ruppeiner geometry for the Kerr black hole in d=5 with double angular momenta.},

doi = {10.1103/PHYSREVD.73.0},

journal = {Physical Review. D, Particles Fields},

number = 2,

volume = 73,

place = {United States},

year = {Sun Jan 15 00:00:00 EST 2006},

month = {Sun Jan 15 00:00:00 EST 2006}

}