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Journal Article•DOI•

The phase transition between caged black holes and black strings

Barak Kol1•
The Racah Institute of Physics1
01 Jan 2006-Physics Reports (North-Holland)-Vol. 422, Iss: 4, pp 119-165
TL;DR: In this paper, a full phase diagram was determined numerically, confirming earlier predictions for a merger of the black-hole and black-string phases and giving very strong evidence that the end-state of the Gregory-Laflamme instability is a black hole (in the dimension range 5 ⩽ D ⌽ 13 ).
About: This article is published in Physics Reports.The article was published on 2006-01-01 and is currently open access. It has received 209 citations till now. The article focuses on the topics: Black string & Black hole.
Citations
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Journal Article•DOI•
Black Holes in Higher Dimensions

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Roberto Emparan1, Harvey S. Reall2•
Catalan Institution for Research and Advanced Studies1, University of Cambridge2
08 Sep 2008-Living Reviews in Relativity
TL;DR: This work discusses black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space, and reviews Myers-Perry solutions, black rings, and solution-generating techniques.
Abstract: We review black-hole solutions of higher-dimensional vacuum gravity and higher-dimensional supergravity theories. The discussion of vacuum gravity is pedagogical, with detailed reviews of Myers-Perry solutions, black rings, and solution-generating techniques. We discuss black-hole solutions of maximal supergravity theories, including black holes in anti-de Sitter space. General results and open problems are discussed throughout.

860 citations

Cites background from "The phase transition between caged ..."

  • ...The instabilities of black strings and black branes [118, 119] have been reviewed in [167, 128], so we shall be brief in this section and only mention the features that are most relevant to our subject....

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Journal Article•DOI•
Mimicking the QCD equation of state with a dual black hole

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Steven S. Gubser1, Abhinav Nellore1•
Princeton University1
29 Oct 2008-Physical Review D
TL;DR: In this paper, the authors present numerical and analytical studies of the equation of state of translationally invariant black hole solutions to five-dimensional gravity coupled to a single scalar.
Abstract: We present numerical and analytical studies of the equation of state of translationally invariant black hole solutions to five-dimensional gravity coupled to a single scalar. As an application, we construct a family of black holes that closely mimics the equation of state of quantum chromodynamics at zero chemical potential.

339 citations

Journal Article•DOI•
A new approach to static numerical relativity and its application to Kaluza–Klein black holes

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Matthew Headrick1, Sam Kitchen2, Toby Wiseman2•
Brandeis University1, Imperial College London2
11 Jan 2010-Classical and Quantum Gravity
TL;DR: In this paper, the authors propose a framework for solving the Einstein equation for static and Euclidean metrics, and demonstrate the use of these methods by studying localized black holes and non-uniform black strings in five-dimensional Kaluza-Klein theory.
Abstract: We propose a framework for solving the Einstein equation for static and Euclidean metrics. First, we address the issue of gauge-fixing by borrowing from the Ricci-flow literature the so-called DeTurck trick, which renders the Einstein equation strictly elliptic and generalizes the usual harmonic-coordinate gauge. We then study two algorithms, Ricci-flow and Newton's method, for solving the resulting Einstein–DeTurck equation. We illustrate the use of these methods by studying localized black holes and non-uniform black strings in five-dimensional Kaluza–Klein theory, improving on previous calculations of their thermodynamic and geometric properties. We study spectra of various operators for these solutions, in particular finding the negative modes of the Lichnerowicz operator. We classify the localized solutions into two branches that meet at a minimum temperature. We find good evidence for a merger between the localized and non-uniform solutions. We also find a narrow window of localized solutions that possess negative modes yet have positive specific heat.

270 citations

Journal Article•DOI•
Black strings, low viscosity fluids, and violation of cosmic censorship.

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Luis Lehner1, Luis Lehner2, Luis Lehner3, Frans Pretorius4•
University of Guelph1, Canadian Institute for Advanced Research2, Perimeter Institute for Theoretical Physics3, Princeton University4
02 Sep 2010-Physical Review Letters
TL;DR: In this paper, the behavior of 5-dimensional black strings subject to the Gregory-Laflamme instability is described, where at intermediate stages the horizon can be described as a sequence of 3-dimensional spherical black holes joined by black string segments.
Abstract: We describe the behavior of 5-dimensional black strings, subject to the Gregory-Laflamme instability. Beyond the linear level, the evolving strings exhibit a rich dynamics, where at intermediate stages the horizon can be described as a sequence of 3-dimensional spherical black holes joined by black string segments. These segments are themselves subject to a Gregory-Laflamme instability, resulting in a self-similar cascade, where ever-smaller satellite black holes form connected by ever-thinner string segments. This behavior is akin to satellite formation in low-viscosity fluid streams subject to the Rayleigh-Plateau instability. The simulation results imply that the string segments will reach zero radius in finite asymptotic time, whence the classical space-time terminates in a naked singularity. Since no fine-tuning is required to excite the instability, this constitutes a generic violation of cosmic censorship.

238 citations

Journal Article•DOI•
The Phase Structure of Higher-Dimensional Black Rings and Black Holes

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Roberto Emparan1, Roberto Emparan2, Troels Harmark3, Vasilis Niarchos4, Niels A. Obers3, Maria J. Rodriguez2 •
Catalan Institution for Research and Advanced Studies1, University of Barcelona2, Niels Bohr Institute3, École Polytechnique4
31 Oct 2007-Journal of High Energy Physics
TL;DR: In this paper, the authors constructed an approximate solution for an asymptotically flat, neutral, thin rotating black ring in any dimension D ≥ 5 by matching the near-horizon solution for a bent boosted black string, to a linearized gravity solution away from the horizon.
Abstract: We construct an approximate solution for an asymptotically flat, neutral, thin rotating black ring in any dimension D ≥ 5 by matching the near-horizon solution for a bent boosted black string, to a linearized gravity solution away from the horizon. The rotating black ring solution has a regular horizon of topology S1 × SD−3 and incorporates the balancing condition of the ring as a zero-tension condition. For D = 5 our method reproduces the thin ring limit of the exact black ring solution. For D ≥ 6 we show that the black ring has a higher entropy than the Myers-Perry black hole in the ultra-spinning regime. By exploiting the correspondence between ultra-spinning black holes and black membranes on a two-torus, we take steps towards qualitatively completing the phase diagram of rotating blackfolds with a single angular momentum. We are led to propose a connection between MP black holes and black rings, and between MP black holes and black Saturns, through merger transitions involving two kinds of `pinched' black holes. More generally, the analogy suggests an infinite number of pinched black holes of spherical topology leading to a complicated pattern of connections and mergers between phases.

226 citations

Cites background from "The phase transition between caged ..."

  • ...the reviews [24, 25] and the recent work [26])....

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References
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Book•
Quantum Mechanics

[...]

Albert Messiah
01 Jan 1961

20,079 citations

Book•
General Relativity

[...]

Robert Wald
01 Jan 1984

8,137 citations

Journal Article•DOI•
Action Integrals and Partition Functions in Quantum Gravity

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Gary W. Gibbons1, Stephen W. Hawking1•
University of Cambridge1
15 May 1977-Physical Review D
TL;DR: In this article, the authors derived finite, purely imaginary values for the actions of the Kerr-Newman solutions and de Sitter space, which they used to evaluate the entropy of these metrics and find that it is always equal to one quarter the area of the event horizon in fundamental units.
Abstract: One can evaluate the action for a gravitational field on a section of the complexified spacetime which avoids the singularities. In this manner we obtain finite, purely imaginary values for the actions of the Kerr-Newman solutions and de Sitter space. One interpretation of these values is that they give the probabilities for finding such metrics in the vacuum state. Another interpretation is that they give the contribution of that metric to the partition function for a grand canonical ensemble at a certain temperature, angular momentum, and charge. We use this approach to evaluate the entropy of these metrics and find that it is always equal to one quarter the area of the event horizon in fundamental units. This agrees with previous derivations by completely different methods. In the case of a stationary system such as a star with no event horizon, the gravitational field has no entropy.

3,067 citations

"The phase transition between caged ..." refers background or methods in this paper

  • ... other thermodynamic variables) and are therefore exothermic (involving latent heat) while for second order and higher the phases are continuously connected and there is no finite release of energy. 18[53] uses definition (3.10), and the equivalence with definition (3.11) is used in a computation. I believe that the third and last definition is implied by the relation between the boundary conditions and t...

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  • ...ves, namely (∂g)(∂g) ∈ I, g∂2g /∈ I where g denotes here a generic metric element. In asymptotically flat spaces I∂ as defined above (3.10) diverges and must be regularized. The standard regularization [53] is done by measuring I relative to flat space. One chooses a large cutoff r = R, where in our case the boundary is Sd−2 R × S 1 L(R) × S 1 β(R), where L(R), β(R) are the periods of the z, t directions,...

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  • ... formalism and the general Landau-Ginzburg theory and then we summarize the results for the system under study. The gravitational free energy. We will use the standard semi-classical15 GibbonsHawking [53] gravitational free energy given by the gravitational action I(gµν; β) = −βF (to be described below) evaluated on a “Euclidean section” of the metric. Since our solutions are static,16 it is straightf...

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  • ...andard Einstein-Hilbert action with an additional boundary term I∂ I = IEH +I∂ (3.8) such that I is stationary on solutions with respect to variations of the metric which preserve the boundary metric [53, 54]. IEH = 1 16πG Z M R , (3.9) 15From a practical point of view all the computations with this action are classical. ~ enters only in the dictionary between the variables of F such as β,A (the periodici...

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Journal Article•DOI•
Thermodynamics of black holes in anti-de Sitter space

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Stephen W. Hawking1, Don N. Page2•
University of Cambridge1, Pennsylvania State University2
01 Dec 1983-Communications in Mathematical Physics
TL;DR: In this paper, it was shown that the canonical ensemble exists for asymptotically anti-de-Sitter space, unlike the case for the case of asymPTotically flat space.
Abstract: The Einstein equations with a negative cosmological constant admit black hole solutions which are asymptotic to anti-de Sitter space. Like black holes in asymptotically flat space, these solutions have thermodynamic properties including a characteristic temperature and an intrinsic entropy equal to one quarter of the area of the event horizon in Planck units. There are however some important differences from the asymptotically flat case. A black hole in anti-de Sitter space has a minimum temperature which occurs when its size is of the order of the characteristic radius of the anti-de Sitter space. For larger black holes the red-shifted temperature measured at infinity is greater. This means that such black holes have positive specific heat and can be in stable equilibrium with thermal radiation at a fixed temperature. It also implies that the canonical ensemble exists for asymptotically anti-de Sitter space, unlike the case for asymptotically flat space. One can also consider the microcanonical ensemble. One can avoid the problem that arises in asymptotically flat space of having to put the system in a box with unphysical perfectly reflecting walls because the gravitational potential of anti-de Sitter space acts as a box of finite volume.

2,923 citations

"The phase transition between caged ..." refers background in this paper

  • ...grams. An example: the Hawking-Page transition. The reader familiar with the phase transition between thermal Anti-de-Sitter (AdS) and large black holes in AdS, known as the “Hawking-Page transition” [61], may benefit from applying the Morse theory ideas above to that context. In the Hawking-Page transition in its canonical ensemble setting, one considers a spacetime with a negative cosmological consta...

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  • ...and will not be discussed here. – 24 – F 1 0 β=β β=β large BH large BH small BH small BH Thermal AdS β β β 0 1 Thermal AdS Figure 11: The free energy and phase diagram for the Hawking-Page transition [61] in AdS space, which is a first order phase transition. At β = β0 the unstable small black hole phase meets the stable large black hole phase and they “annihilate” according to our ”basic vertex” rule....

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Journal Article•DOI•
Black holes in higher dimensional space-times

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Robert C. Myers1, Malcolm J. Perry1•
Princeton University1
01 Dec 1986-Annals of Physics
TL;DR: In this paper, a new family of solutions were found which describe spinning black holes in higher dimensional space-times, which are similar to the familiar Kerr and Schwarzschild metrics which are recovered for N = 3.

2,190 citations

"The phase transition between caged ..." refers background in this paper

  • ...Set-up and formulation of questions 5 2.1 Background 5 2.2 Phases 6 2.3 Gregory-Laflamme instability 8 2.4 Issues 11...

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  • ...On the contrary, the theory is independent of D, and D should be considered as a parameter....

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The Phase Transition between Caged Black Holes and Black Strings - A Review

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Black strings and p -branes are unstable

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10 May 1993-Physical Review Letters
Ruth Gregory, Raymond Laflamme
Instabilities of black strings and branes

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29 Mar 2007-Classical and Quantum Gravity
Troels Harmark, Vasilis Niarchos, Niels A. Obers
On non-uniform black branes

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07 Oct 2002-Classical and Quantum Gravity
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Static axisymmetric vacuum solutions and non-uniform black strings

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03 Mar 2003-Classical and Quantum Gravity
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