Curvature corrections and topology change transition in brane-black hole systems: A perturbative approach

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 does not lead to regular solutions 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 presented perturbative approach 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. For the general case, a different, non-perturbative 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.

Static configurations and evolution of higher dimensional brane-dilaton black hole system

“…were studied [29][30][31]. The last moments of a mini black hole escaping from a brane were examined in [32].…”

“…Thus, the analysis of the static configurations of the studied system is relevant for such a brane present within it. The problem of thick branes within the geometric construction is a subtle one and would require calculations based on perturbative corrections [29][30][31]. The assumption that the brane is static and spherically symmetric results in an O(D − 1) symmetry of its world sheet.…”

Piercing of domain walls: new mechanism of gravitational radiation

“…These effects can be regarded as topological phase transitions. Other aspects of such transitions in the composite braneblack hole systems were studied in [19,[23][24][25][26][27]. In the context of the braneworld models, the interaction of black holes with DWs attracted much attention in connection with the conjectured creation of black holes in particle collisions on the brane and their possible escape into the bulk [28][29][30].…”

Branestrahlung: Radiation in the particle-brane collision

“…More recently, the general development of the theory of branes in the superstring setting stimulated investigation of other aspects of this interaction, such as collisions of domain walls and other branes with black holes [4][5][6]. Especially interesting is the process of perforation, which was suggested as a new mechanism of domain-wall destruction in the early Universe [4,7,8].…”