# Thermodynamic properties of asymptotically Reissner–Nordström black holes

## Abstract

Motivated by possible relation between Born–Infeld type nonlinear electrodynamics and an effective low-energy action of open string theory, asymptotically Reissner–Nordström black holes whose electric field is described by a nonlinear electrodynamics (NLED) are studied. We take into account a four dimensional topological static black hole ansatz and solve the field equations, exactly, in terms of the NLED as a matter field. The main goal of this paper is investigation of thermodynamic properties of the obtained black holes. Moreover, we calculate the heat capacity and find that the nonlinearity affects the minimum size of stable black holes. We also use Legendre-invariant metric proposed by Quevedo to obtain scalar curvature divergences. We find that the singularities of the Ricci scalar in Geometrothermodynamics (GTD) method take place at the Davies points. -- Highlights: •We examine the thermodynamical properties of black holes in Einstein gravity with nonlinear electrodynamics. •We investigate thermodynamic stability and discuss about the size of stable black holes. •We obtain analytical solutions of higher dimensional theory.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22314831

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Annals of Physics (New York); Journal Volume: 346; Journal Issue: Complete; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANALYTICAL SOLUTION; BLACK HOLES; BORN-INFELD THEORY; ELECTRIC FIELDS; ELECTRODYNAMICS; FIELD EQUATIONS; FOUR-DIMENSIONAL CALCULATIONS; GRAVITATION; METRICS; NONLINEAR PROBLEMS; SCALARS; SINGULARITY; SPECIFIC HEAT; STABILITY; STRING MODELS; STRING THEORY; TOPOLOGY

### Citation Formats

```
Hendi, S.H., E-mail: hendi@shirazu.ac.ir.
```*Thermodynamic properties of asymptotically Reissner–Nordström black holes*. United States: N. p., 2014.
Web. doi:10.1016/J.AOP.2014.04.006.

```
Hendi, S.H., E-mail: hendi@shirazu.ac.ir.
```*Thermodynamic properties of asymptotically Reissner–Nordström black holes*. United States. doi:10.1016/J.AOP.2014.04.006.

```
Hendi, S.H., E-mail: hendi@shirazu.ac.ir. Tue .
"Thermodynamic properties of asymptotically Reissner–Nordström black holes". United States. doi:10.1016/J.AOP.2014.04.006.
```

```
@article{osti_22314831,
```

title = {Thermodynamic properties of asymptotically Reissner–Nordström black holes},

author = {Hendi, S.H., E-mail: hendi@shirazu.ac.ir},

abstractNote = {Motivated by possible relation between Born–Infeld type nonlinear electrodynamics and an effective low-energy action of open string theory, asymptotically Reissner–Nordström black holes whose electric field is described by a nonlinear electrodynamics (NLED) are studied. We take into account a four dimensional topological static black hole ansatz and solve the field equations, exactly, in terms of the NLED as a matter field. The main goal of this paper is investigation of thermodynamic properties of the obtained black holes. Moreover, we calculate the heat capacity and find that the nonlinearity affects the minimum size of stable black holes. We also use Legendre-invariant metric proposed by Quevedo to obtain scalar curvature divergences. We find that the singularities of the Ricci scalar in Geometrothermodynamics (GTD) method take place at the Davies points. -- Highlights: •We examine the thermodynamical properties of black holes in Einstein gravity with nonlinear electrodynamics. •We investigate thermodynamic stability and discuss about the size of stable black holes. •We obtain analytical solutions of higher dimensional theory.},

doi = {10.1016/J.AOP.2014.04.006},

journal = {Annals of Physics (New York)},

number = Complete,

volume = 346,

place = {United States},

year = {Tue Jul 15 00:00:00 EDT 2014},

month = {Tue Jul 15 00:00:00 EDT 2014}

}