# Thermodynamics of asymptotically flat charged black holes in third order Lovelock gravity

## Abstract

We present a new class of asymptotically flat charge static solutions in third order Lovelock gravity. These solutions present black hole solutions with two inner and outer event horizons, extreme black holes, or naked singularities provided the parameters of the solutions are chosen suitable. We find that the uncharged asymptotically flat solutions can present black holes with two inner and outer horizons. This kind of solution does not exist in Einstein or Gauss-Bonnet gravity, and it is a special effect in third order Lovelock gravity. We compute temperature, entropy, charge, electric potential, and mass of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We also perform a stability analysis by computing the determinant of the Hessian matrix of the mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that there exists only an intermediate stable phase.

- Authors:

- Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz 71454 (Iran, Islamic Republic of)
- (RIAAM), Maragha (Iran, Islamic Republic of)

- Publication Date:

- OSTI Identifier:
- 20774536

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.72.124015; (c) 2005 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; BLACK HOLES; COSMOLOGY; ENTROPY; GENERAL RELATIVITY THEORY; GRAVITATION; MASS; MATHEMATICAL SOLUTIONS; SINGULARITY; SPACE-TIME; STABILITY; STRING MODELS; THERMODYNAMICS

### Citation Formats

```
Dehghani, M.H., Research Institute for Astrophysics and Astronomy of Maragha, and Shamirzaie, M.
```*Thermodynamics of asymptotically flat charged black holes in third order Lovelock gravity*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevD.72.124015.

```
Dehghani, M.H., Research Institute for Astrophysics and Astronomy of Maragha, & Shamirzaie, M.
```*Thermodynamics of asymptotically flat charged black holes in third order Lovelock gravity*. United States. doi:10.1103/PhysRevD.72.124015.

```
Dehghani, M.H., Research Institute for Astrophysics and Astronomy of Maragha, and Shamirzaie, M. Thu .
"Thermodynamics of asymptotically flat charged black holes in third order Lovelock gravity". United States.
doi:10.1103/PhysRevD.72.124015.
```

```
@article{osti_20774536,
```

title = {Thermodynamics of asymptotically flat charged black holes in third order Lovelock gravity},

author = {Dehghani, M.H. and Research Institute for Astrophysics and Astronomy of Maragha and Shamirzaie, M.},

abstractNote = {We present a new class of asymptotically flat charge static solutions in third order Lovelock gravity. These solutions present black hole solutions with two inner and outer event horizons, extreme black holes, or naked singularities provided the parameters of the solutions are chosen suitable. We find that the uncharged asymptotically flat solutions can present black holes with two inner and outer horizons. This kind of solution does not exist in Einstein or Gauss-Bonnet gravity, and it is a special effect in third order Lovelock gravity. We compute temperature, entropy, charge, electric potential, and mass of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We also perform a stability analysis by computing the determinant of the Hessian matrix of the mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that there exists only an intermediate stable phase.},

doi = {10.1103/PhysRevD.72.124015},

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

number = 12,

volume = 72,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}