# Higher-dimensional black holes with a conformally invariant Maxwell source

## Abstract

We consider an action for an Abelian gauge field for which the density is given by a power of the Maxwell Lagrangian. In d spacetime dimensions this action is shown to enjoy conformal invariance if the power is chosen as d/4. We take advantage of this conformal invariance to derive black hole solutions electrically charged with a purely radial electric field. Since we are considering a power of the Maxwell density, the black hole solutions exist only for dimensions which are multiples of four. The expression for the electric field does not depend on the dimension and corresponds to the four-dimensional Reissner-Nordstroem field. Using the Hamiltonian action we identify the mass and the electric charge of these black hole solutions.

- Authors:

- Instituto de Matematica y Fisica, Universidad de Talca, Casilla 747, Talca (Chile) and Centro de Estudios Cientificos (CECS), Casilla 1469, Valdivia (Chile)
- (CECS), Casilla 1469, Valdivia (Chile)

- Publication Date:

- OSTI Identifier:
- 21010955

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.75.027502; (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; ACTION INTEGRAL; BLACK HOLES; CONFORMAL INVARIANCE; COSMOLOGY; DENSITY; ELECTRIC CHARGES; ELECTRIC FIELDS; FOUR-DIMENSIONAL CALCULATIONS; GAUGE INVARIANCE; HAMILTONIANS; LAGRANGIAN FUNCTION; MATHEMATICAL SOLUTIONS; QUANTUM FIELD THEORY; SPACE-TIME

### Citation Formats

```
Hassaiene, Mokhtar, Martinez, Cristian, and Centro de Estudios Cientificos.
```*Higher-dimensional black holes with a conformally invariant Maxwell source*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.027502.

```
Hassaiene, Mokhtar, Martinez, Cristian, & Centro de Estudios Cientificos.
```*Higher-dimensional black holes with a conformally invariant Maxwell source*. United States. doi:10.1103/PHYSREVD.75.027502.

```
Hassaiene, Mokhtar, Martinez, Cristian, and Centro de Estudios Cientificos. Mon .
"Higher-dimensional black holes with a conformally invariant Maxwell source". United States.
doi:10.1103/PHYSREVD.75.027502.
```

```
@article{osti_21010955,
```

title = {Higher-dimensional black holes with a conformally invariant Maxwell source},

author = {Hassaiene, Mokhtar and Martinez, Cristian and Centro de Estudios Cientificos},

abstractNote = {We consider an action for an Abelian gauge field for which the density is given by a power of the Maxwell Lagrangian. In d spacetime dimensions this action is shown to enjoy conformal invariance if the power is chosen as d/4. We take advantage of this conformal invariance to derive black hole solutions electrically charged with a purely radial electric field. Since we are considering a power of the Maxwell density, the black hole solutions exist only for dimensions which are multiples of four. The expression for the electric field does not depend on the dimension and corresponds to the four-dimensional Reissner-Nordstroem field. Using the Hamiltonian action we identify the mass and the electric charge of these black hole solutions.},

doi = {10.1103/PHYSREVD.75.027502},

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

number = 2,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}