# Extremal black holes in D=4 Gauss-Bonnet gravity

## Abstract

We show that four-dimensional Einstein-Maxwell-dilaton-Gauss-Bonnet gravity admits asymptotically flat black hole solutions with a degenerate event horizon of the Reissner-Nordstroem type AdS{sub 2}xS{sup 2}. Such black holes exist for the dilaton coupling constant within the interval 0{<=}a{sup 2}<a{sub cr}{sup 2}. Black holes must be endowed with an electric charge and (possibly) with magnetic charge (dyons) but they cannot be purely magnetic. Purely electric solutions are constructed numerically and the critical dilaton coupling is determined a{sub cr}{approx_equal}0.488 219 703. For each value of the dilaton coupling a within this interval and for a fixed value of the Gauss-Bonnet coupling {alpha} we have a family of black holes parametrized by their electric charge. The relation between the mass, the electric charge, and the dilaton charge at both ends of the allowed interval of a is reminiscent of the Bogomol'nyi-Prasad-Sommerfield condition for dilaton black holes in the Einstein-Maxwell-dilaton theory. The entropy of the dilaton-Gauss-Bonnet extremal black holes is twice the Bekenstein-Hawking entropy.

- Authors:

- Department of Physics, National Central University, Chungli 320, Taiwan (China)
- (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 21020399

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 8; Other Information: DOI: 10.1103/PhysRevD.75.084030; (c) 2007 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; COUPLING; COUPLING CONSTANTS; DYONS; ELECTRIC CHARGES; ENTROPY; FOUR-DIMENSIONAL CALCULATIONS; GRAVITATION; MASS; MATHEMATICAL SOLUTIONS; QUANTUM FIELD THEORY

### Citation Formats

```
Chen, C.-M., Gal'tsov, Dmitri V., Orlov, Dmitry G., Department of Theoretical Physics, Moscow State University, 119899, Moscow,, and Department of Physics, National Central University, Chungli 320, Taiwan and Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya Street, Moscow 119361.
```*Extremal black holes in D=4 Gauss-Bonnet gravity*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.084030.

```
Chen, C.-M., Gal'tsov, Dmitri V., Orlov, Dmitry G., Department of Theoretical Physics, Moscow State University, 119899, Moscow,, & Department of Physics, National Central University, Chungli 320, Taiwan and Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya Street, Moscow 119361.
```*Extremal black holes in D=4 Gauss-Bonnet gravity*. United States. doi:10.1103/PHYSREVD.75.084030.

```
Chen, C.-M., Gal'tsov, Dmitri V., Orlov, Dmitry G., Department of Theoretical Physics, Moscow State University, 119899, Moscow,, and Department of Physics, National Central University, Chungli 320, Taiwan and Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya Street, Moscow 119361. Sun .
"Extremal black holes in D=4 Gauss-Bonnet gravity". United States.
doi:10.1103/PHYSREVD.75.084030.
```

```
@article{osti_21020399,
```

title = {Extremal black holes in D=4 Gauss-Bonnet gravity},

author = {Chen, C.-M. and Gal'tsov, Dmitri V. and Orlov, Dmitry G. and Department of Theoretical Physics, Moscow State University, 119899, Moscow, and Department of Physics, National Central University, Chungli 320, Taiwan and Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya Street, Moscow 119361},

abstractNote = {We show that four-dimensional Einstein-Maxwell-dilaton-Gauss-Bonnet gravity admits asymptotically flat black hole solutions with a degenerate event horizon of the Reissner-Nordstroem type AdS{sub 2}xS{sup 2}. Such black holes exist for the dilaton coupling constant within the interval 0{<=}a{sup 2}<a{sub cr}{sup 2}. Black holes must be endowed with an electric charge and (possibly) with magnetic charge (dyons) but they cannot be purely magnetic. Purely electric solutions are constructed numerically and the critical dilaton coupling is determined a{sub cr}{approx_equal}0.488 219 703. For each value of the dilaton coupling a within this interval and for a fixed value of the Gauss-Bonnet coupling {alpha} we have a family of black holes parametrized by their electric charge. The relation between the mass, the electric charge, and the dilaton charge at both ends of the allowed interval of a is reminiscent of the Bogomol'nyi-Prasad-Sommerfield condition for dilaton black holes in the Einstein-Maxwell-dilaton theory. The entropy of the dilaton-Gauss-Bonnet extremal black holes is twice the Bekenstein-Hawking entropy.},

doi = {10.1103/PHYSREVD.75.084030},

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

number = 8,

volume = 75,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}