# Quasinormal modes and stability criterion of dilatonic black holes in 1+1 and 4+1 dimensions

## Abstract

We study the stability of black holes that are solutions of the dilaton gravity derived from string-theoretical models in two and five dimensions under scalar field perturbations, using the Quasinormal Modes (QNMs) approach. In order to find the QNMs corresponding to a black hole geometry, we consider perturbations described by a massive scalar field nonminimally coupled to gravity. We find that the QNMs frequencies turn out to be pure imaginary leading to purely damped modes, in the range 0<{zeta}<1/4 of nonminimal coupling constant ({zeta}), and the QNMs acquires a real part if {zeta}>1/4 that is in agreement with the literature of dilatonic black holes. Our result exhibits the unstable behavior of the considered geometry against scalar perturbations. We study the instability for different values of nonminimal coupling constant. We extend our results to the 4+1 dimensional dilatonic black hole, where the metric is the product of a two-dimensional asymptotically flat geometry and a three-sphere with constant radius, which are completely decoupled from each other. The exact solution for the QNMs was obtained in the five-dimensional case.

- Authors:

- Departamento de Fisica, Universidad de Concepcion, Casilla 160 C, Concepcion (Chile)
- Instituto de Fisica, Pontificia Universidad Catolica de Valparaiso, Casilla 4950, Valparaiso (Chile)

- Publication Date:

- OSTI Identifier:
- 21020390

- 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.75.084021; (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 CONSTANTS; DISTURBANCES; EXACT SOLUTIONS; GEOMETRY; GRAVITATION; INSTABILITY; QUANTUM FIELD THEORY; SCALAR FIELDS; STABILITY; STRING MODELS

### Citation Formats

```
Becar, Ramon, Lepe, Samuel, and Saavedra, Joel.
```*Quasinormal modes and stability criterion of dilatonic black holes in 1+1 and 4+1 dimensions*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.084021.

```
Becar, Ramon, Lepe, Samuel, & Saavedra, Joel.
```*Quasinormal modes and stability criterion of dilatonic black holes in 1+1 and 4+1 dimensions*. United States. doi:10.1103/PHYSREVD.75.084021.

```
Becar, Ramon, Lepe, Samuel, and Saavedra, Joel. Sun .
"Quasinormal modes and stability criterion of dilatonic black holes in 1+1 and 4+1 dimensions". United States.
doi:10.1103/PHYSREVD.75.084021.
```

```
@article{osti_21020390,
```

title = {Quasinormal modes and stability criterion of dilatonic black holes in 1+1 and 4+1 dimensions},

author = {Becar, Ramon and Lepe, Samuel and Saavedra, Joel},

abstractNote = {We study the stability of black holes that are solutions of the dilaton gravity derived from string-theoretical models in two and five dimensions under scalar field perturbations, using the Quasinormal Modes (QNMs) approach. In order to find the QNMs corresponding to a black hole geometry, we consider perturbations described by a massive scalar field nonminimally coupled to gravity. We find that the QNMs frequencies turn out to be pure imaginary leading to purely damped modes, in the range 0<{zeta}<1/4 of nonminimal coupling constant ({zeta}), and the QNMs acquires a real part if {zeta}>1/4 that is in agreement with the literature of dilatonic black holes. Our result exhibits the unstable behavior of the considered geometry against scalar perturbations. We study the instability for different values of nonminimal coupling constant. We extend our results to the 4+1 dimensional dilatonic black hole, where the metric is the product of a two-dimensional asymptotically flat geometry and a three-sphere with constant radius, which are completely decoupled from each other. The exact solution for the QNMs was obtained in the five-dimensional case.},

doi = {10.1103/PHYSREVD.75.084021},

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}

}