Towards the final fate of an unstable black string

Choptuik, Matthew W.; Lehner, Luis; Olabarrieta, Ignacio; Petryk, Roman; Pretorius, Frans; Villegas, Hugo

doi:10.1103/physrevd.68.044001

Cited by 109 publications

(194 citation statements)

References 27 publications

(54 reference statements)

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“…However, another technique which has been successfully used in previous work in numerical relativity, see e.g. [10,37], involves compactification of the spatial domain. Paralleling the experience of these earlier studies, we have found that compactifying the radial direction and imposing the (exact) Dirichlet conditions (4.10) at the edge of the domain works well, provided that we use sufficient dissipation.…”

Section: Coordinates and Boundary Conditionsmentioning

confidence: 99%

Generalized harmonic formulation in spherical symmetry

Sorkin

Choptuik

2009

Gen Relativ Gravit

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In this pedagogically structured article, we describe a generalized harmonic (GH) formulation of the Einstein equations in spherical symmetry which is regular at the origin. The GH approach has attracted significant attention in numerical relativity over the past few years, especially as applied to the problem of binary inspiral and merger. A key issue when using the technique is the choice of the gauge source functions, and recent work has provided several prescriptions for gauge drivers designed to evolve these functions in a controlled way. We numerically investigate the parameter spaces of some of these drivers in the context of fully non-linear collapse of a real, massless scalar field, and determine nearly optimal parameter settings for specific situations. Surprisingly, we find that many of the drivers that perform well in 3 + 1 calculations that use Cartesian coordinates, are considerably less effective in spherical symmetry, where some of them are, in fact, unstable.

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Section: Coordinates and Boundary Conditionsmentioning

confidence: 99%

Generalized harmonic formulation in spherical symmetry

Sorkin

Choptuik

2009

Gen Relativ Gravit

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“…This fact suggests a natural definition of the strongly non-linear regime as a situation when these variables are close to saturation. 2 Recently, intriguing proposals regarding the local geometry near the "waist" of the extremely non-uniform strings have been put forward by Kol [3,20]. Specifically, in [3] Kol advocates that locally the merger spacetime is cone-like, and moreover in D ≤ 10 the local slightly off-merger metric and its functions have power-law dependence on parametric distance from the critical (merger) cone.…”

Section: Introductionmentioning

confidence: 99%

Nonuniform black strings in various dimensions

Sorkin

2006

Phys. Rev. D

112

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The nonuniform black strings branch, which emerges from the critical GregoryLaflamme string, is numerically constructed in dimensions 6 ≤ D ≤ 11 and extended into the strongly non-linear regime. All the solutions are more massive and less entropic than the marginal string. We find the asymptotic values of the mass, the entropy and other physical variables in the limit of large horizon deformations. By explicit metric comparison we verify that the local geometry around the "waist" of our most nonuniform solutions is cone-like with less than 10% deviation. We find evidence that in this regime the characteristic length scale has a power-law dependence on a parameter along the branch of the solutions, and estimate the critical exponent.

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“…In Kaluza-Klein space-times, it is well-known that there exist both uniform and nonuniform black strings with the same mass µ [26,10,11,27,13,16] (see also [28,29,30]). There is also a family of topologically spherical black holes localized on the Kaluza-Klein circle [17,14,15,22,23].…”

Section: Introductionmentioning

confidence: 99%

Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes

Elvang¹,

Harmark²,

Obers³

2005

J. High Energy Phys.

137

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We construct and analyze a large class of exact five-and six-dimensional regular and static solutions of the vacuum Einstein equations. These solutions describe sequences of KaluzaKlein bubbles and black holes, placed alternately so that the black holes are held apart by the bubbles. Asymptotically the solutions are Minkowski-space times a circle, i.e. KaluzaKlein space, so they are part of the (µ, n) phase diagram introduced in hep-th/0309116. In particular, they occupy a hitherto unexplored region of the phase diagram, since their relative tension exceeds that of the uniform black string. The solutions contain bubbles and black holes of various topologies, including six-dimensional black holes with ring topology S 3 × S 1 and tuboid topology S 2 × S 1 × S 1 . The bubbles support the S 1 's of the horizons against gravitational collapse. We find two maps between solutions, one that relates fiveand six-dimensional solutions, and another that relates solutions in the same dimension by interchanging bubbles and black holes. To illustrate the richness of the phase structure and the non-uniqueness in the (µ, n) phase diagram, we consider in detail particular examples of the general class of solutions.

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Towards the final fate of an unstable black string

Cited by 109 publications

References 27 publications

Generalized harmonic formulation in spherical symmetry

Generalized harmonic formulation in spherical symmetry

Nonuniform black strings in various dimensions

Sequences of Bubbles and Holes: New Phases of Kaluza-Klein Black Holes

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