### Abstract

We consider curvature corrections to static, axisymmetric Dirac-Nambu-Goto membranes embedded into a spherically symmetric black hole spacetime with arbitrary number of dimensions. Since the next to leading order corrections in the effective brane action are quadratic in the brane thickness ℓ, we adopt a linear perturbation approach in ℓ^{2}. The perturbations are general in the sense that they are not restricted to the Rindler zone nor to the near-critical solutions of the unperturbed system. As a result, an unexpected asymmetry in the perturbed system is found. In configurations, where the brane does not cross the black hole horizon, the perturbative approach used here does not lead to regular solutions of the perturbation equation if the number of the brane's spacetime dimensions D > 3. This condition, however, does not hold for the horizon crossing solutions. Consequently we argue that the perturbative approaches used here breaks down for subcritical type solutions near the axis of the system for D > 3. Nevertheless, we can discuss topology-changing phase transitions in cases when D = 2 or 3, i.e. when the brane is a 1-dimensional string or a 2-dimensional sheet, respectively. In the general case, a different approach should be sought. Based on the energy properties of those branes that are quasi-statically evolved from the equatorial configuration, we illustrate the results of the phase transition in the case of a D = 3 brane. It is found that small thickness perturbations do not modify the order of the transition, i.e. it remains first order just as in the case of vanishing thickness.

Original language | English |
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Pages | 133-136 |

Number of pages | 4 |

Publication status | Published - 2009 Dec 1 |

Externally published | Yes |

Event | 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009 - Tokyo, Japan Duration: 2009 Nov 30 → 2009 Dec 4 |

### Other

Other | 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009 |
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Country | Japan |

City | Tokyo |

Period | 09/11/30 → 09/12/4 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Beyond the dirac-nambu-goto approximation in brane-black hole systems*. 133-136. Paper presented at 19th Workshop on General Relativity and Gravitation in Japan, JGRG 2009, Tokyo, Japan.

**Beyond the dirac-nambu-goto approximation in brane-black hole systems.** / Czinner, Viktor G.; Flachi, Antonino.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - Beyond the dirac-nambu-goto approximation in brane-black hole systems

AU - Czinner, Viktor G.

AU - Flachi, Antonino

PY - 2009/12/1

Y1 - 2009/12/1

N2 - We consider curvature corrections to static, axisymmetric Dirac-Nambu-Goto membranes embedded into a spherically symmetric black hole spacetime with arbitrary number of dimensions. Since the next to leading order corrections in the effective brane action are quadratic in the brane thickness ℓ, we adopt a linear perturbation approach in ℓ2. The perturbations are general in the sense that they are not restricted to the Rindler zone nor to the near-critical solutions of the unperturbed system. As a result, an unexpected asymmetry in the perturbed system is found. In configurations, where the brane does not cross the black hole horizon, the perturbative approach used here does not lead to regular solutions of the perturbation equation if the number of the brane's spacetime dimensions D > 3. This condition, however, does not hold for the horizon crossing solutions. Consequently we argue that the perturbative approaches used here breaks down for subcritical type solutions near the axis of the system for D > 3. Nevertheless, we can discuss topology-changing phase transitions in cases when D = 2 or 3, i.e. when the brane is a 1-dimensional string or a 2-dimensional sheet, respectively. In the general case, a different approach should be sought. Based on the energy properties of those branes that are quasi-statically evolved from the equatorial configuration, we illustrate the results of the phase transition in the case of a D = 3 brane. It is found that small thickness perturbations do not modify the order of the transition, i.e. it remains first order just as in the case of vanishing thickness.

AB - We consider curvature corrections to static, axisymmetric Dirac-Nambu-Goto membranes embedded into a spherically symmetric black hole spacetime with arbitrary number of dimensions. Since the next to leading order corrections in the effective brane action are quadratic in the brane thickness ℓ, we adopt a linear perturbation approach in ℓ2. The perturbations are general in the sense that they are not restricted to the Rindler zone nor to the near-critical solutions of the unperturbed system. As a result, an unexpected asymmetry in the perturbed system is found. In configurations, where the brane does not cross the black hole horizon, the perturbative approach used here does not lead to regular solutions of the perturbation equation if the number of the brane's spacetime dimensions D > 3. This condition, however, does not hold for the horizon crossing solutions. Consequently we argue that the perturbative approaches used here breaks down for subcritical type solutions near the axis of the system for D > 3. Nevertheless, we can discuss topology-changing phase transitions in cases when D = 2 or 3, i.e. when the brane is a 1-dimensional string or a 2-dimensional sheet, respectively. In the general case, a different approach should be sought. Based on the energy properties of those branes that are quasi-statically evolved from the equatorial configuration, we illustrate the results of the phase transition in the case of a D = 3 brane. It is found that small thickness perturbations do not modify the order of the transition, i.e. it remains first order just as in the case of vanishing thickness.

UR - http://www.scopus.com/inward/record.url?scp=84887428456&partnerID=8YFLogxK

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M3 - Paper

AN - SCOPUS:84887428456

SP - 133

EP - 136

ER -