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An Infinite-Dimensional Family of Black-Hole Microstate Geometries
High Energy Physics - Theory · Submitted 17 Jun 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We construct the first explicit, smooth, horizonless black-hole microstate geometry whose moduli space is described by an arbitrary function of one variable and is thus infinite-dimensional.
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The abstract, sentence by sentence
We construct the first explicit, smooth, horizonless black-hole microstate geometry whose moduli space is described by an arbitrary function of one variable and is thus infinite-dimensional. This is achieved by constructing the scalar Green function on a simple D6 anti-D6 background, and using this Green function to obtain the fully back-reacted solution for a supertube with varying charge density in this background. We show that this supertube can store parametrically more entropy than in flat space, confirming the entropy enhancement mechanism that was predicted using brane probes. We also show that all the local properties of the fully back-reacted solution can, in fact, be obtained using the DBI action of an appropriate brane probe. In particular, the supergravity and the DBI analysis yield identical functional bubble equations that govern the relative locations of the centers. This indicates that there is a non-renormalization theorem that protects these functional equations as one moves in moduli space. Our construction creates configurations that are beyond the scope of recent arguments that appear to put strong limits on the entropy that can be found in smooth supergravity solutions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We construct the first explicit, smooth, horizonless black-hole microstate geometry whose moduli space is described by an arbitrary function of one variable and is thus infinite-dimensional. | contribution 0.85 | 0.97 | 0.90 | asserted 1.00 |
| s1 | This is achieved by constructing the scalar Green function on a simple D6 anti-D6 background, and using this Green function to obtain the fully back-reacted solution for a supertube with varying charge density in this background. | method 1.00 | 0.95 | 0.06 | asserted 1.00 |
| s2 | We show that this supertube can store parametrically more entropy than in flat space, confirming the entropy enhancement mechanism that was predicted using brane probes. | result 0.98 | 0.93 | 0.17 | asserted 1.00 |
| s3 | We also show that all the local properties of the fully back-reacted solution can, in fact, be obtained using the DBI action of an appropriate brane probe. | result 0.91 | 0.93 | 0.06 | asserted 1.00 |
| s4 | In particular, the supergravity and the DBI analysis yield identical functional bubble equations that govern the relative locations of the centers. | result 1.00 | 0.92 | 0.09 | asserted 1.00 |
| s5 | This indicates that there is a non-renormalization theorem that protects these functional equations as one moves in moduli space. | interpretation 1.00 | 0.60 | 0.10 | hedged possibility 0.99 |
| s6 | Our construction creates configurations that are beyond the scope of recent arguments that appear to put strong limits on the entropy that can be found in smooth supergravity solutions. | interpretation 0.76 | 0.77 | 0.16 | asserted 0.93 |
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The paper
Original abstract
We construct the first explicit, smooth, horizonless black-hole microstate geometry whose moduli space is described by an arbitrary function of one variable and is thus infinite-dimensional. This is achieved by constructing the scalar Green function on a simple D6 anti-D6 background, and using this Green function to obtain the fully back-reacted solution for a supertube with varying charge density in this background. We show that this supertube can store parametrically more entropy than in flat space, confirming the entropy enhancement mechanism that was predicted using brane probes. We also show that all the local properties of the fully back-reacted solution can, in fact, be obtained using the DBI action of an appropriate brane probe. In particular, the supergravity and the DBI analysis yield identical functional bubble equations that govern the relative locations of the centers. This indicates that there is a non-renormalization theorem that protects these functional equations as one moves in moduli space. Our construction creates configurations that are beyond the scope of recent arguments that appear to put strong limits on the entropy that can be found in smooth supergravity solutions.
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References
How later papers used it
59 later papers cite it
1 paper by the same authors is listed below: 1 used its method or tool.
Uses its method or tool 1 of 2 papers with this label · 1 by the same authors
By the same authors
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Followed this paper's discussion of wiggling supertubes exactly in constructing regular solutions.
Doubly-Fluctuating BPS Solutions in Six Dimensions (2013) (same authors) · 0.94 · paraphrased: the licence does not allow quoting
How the literature uses it
59 arXiv papers cite this in 106 sentences
Papers citing it · 74 sentences without a confident label
Builds on it 1 paper
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The first step will be to allow the electric charge sources in ([ref]) to be $ψ$-dependent much as in [ref] , however here these charges will oscillate into other species of M2-brane charge.
On the Oscillation of Species · Some simple oscillating solutions · 0.87
Uses its method or tool 2 papers
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As discussed in detail in [ref] , regularity near the supertube will impose constraints on the charge densities in the $H_j$, $L_3$ and $M$ and there will be one remaining, freely choosable charge density function, $ρ_+(ψ)$, at this point.
Doubly-Fluctuating BPS Solutions in Six Dimensions · A specific example · 0.80
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To see this, we apply a spectral flow and spectral interchange in sequence: [equation] The set of harmonic functions solving the first layer BPS equations becomes[We follow the conventions of [ref] .]: [equation] The oscillating function $L_1$ can be understood as the oscillating field strength sourced by the charge density $ρ_1$ at the supertube location $r=0$ [ref] : [equation] where $Ĝ$ is the Green function on the the base, and for a general GH geometry such function was constructed in [ref] .
Multi-center Superstrata · Geometries with AdS$_3×$S$^3$ asymptotics · 0.89
Uses its data or values 1 paper
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The entropy of these solutions grows with the charges as $N^5/4$ [ref] , which is more than all other known supergravity solutions, but is still less than the black hole entropy growth, $N^3/2$.
Black-Hole Entropy from Supergravity Superstrata States · Black-hole microstate structure · 0.82
Compares with it 2 papers
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Similarly, the entropy of the largest known class of horizonless microstate geometries [ref] is based on placing supertubes at the bottom of a microstate geometry with a long but finite throat and absorbing them into the background; the result does not scale with the charges as rapidly as the BTZ black hole entropy (though that deficiency could be due to an insufficiently general ansatz for the shape modes of the supertube [ref] ).
Hair-brane Ideas on the Horizon · Discussion · 0.88
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This scaling is also less than the scaling of the total number of Bena-Warner multi-centered microstate geometries, which has been argued to be $S_Bena-Warner∼Q^5/4$ [ref] .
Probing Black Hole Microstate Evolution with Networks and Random Walks · Discussion · 0.92
Cites it as background 21 papers
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The BPS solutions in these circumstances have been discussed in [ref] .
On the Oscillation of Species · The supersymmetry conditions · 0.87
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Historically, the quest for understanding the black hole degrees of freedom has been pursued from the opposite direction: people have first constructed solutions with black-hole charges that do not have a horizon and that exist in the same regime of parameters as the classical black hole solution [ref] .
The (amazing) Super-Maze · Introduction · 0.90
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An (incomplete) list of solutions that have the same types of charges as these black holes can be found in [ref] .
Resolving the Structure of Black Holes: Philosophizing with a Hammer · Introduction · 0.82
What it cites · 69 sentences without a confident label
Builds on 5 papers
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We have thus generalized the results of [ref] to completely general, fluctuating electric charge densities.
Black Rings in Taub-NUT · The general back-reacted solution with fluctuating electric charge densities · 1.00
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We have thus generalized the results of [ref] to completely general, fluctuating electric charge densities.
General Concentric Black Rings · The general back-reacted solution with fluctuating electric charge densities · 1.00
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We have thus generalized the results of [ref] to completely general, fluctuating electric charge densities.
Bubbling Supertubes and Foaming Black Holes · The general back-reacted solution with fluctuating electric charge densities · 1.00
Uses the method or tool of 9 papers
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Our goal here is to obtain the scalar Green function for the ambi-polar GH base considered above, and construct this Green function in such a manner that it can be used to create five-dimensional solutions by the methods outlined in [ref] .
One Ring to Rule Them All ... and in the Darkness Bind Them? · The strategy: reducing a Green function from five to four dimensions · 0.96
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The first step is to solve the first BPS equation in exactly the same manner as for GH base spaces, [ref] and for this it is convenient to introduce the vielbeins:
Black Holes, Black Rings and their Microstates · The general back-reacted solution with fluctuating electric charge densities · 0.95
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The first step is to solve the first BPS equation in exactly the same manner as for GH base spaces, [ref] and for this it is convenient to introduce the vielbeins:
Black Rings in Taub-NUT · The general back-reacted solution with fluctuating electric charge densities · 0.95
Compares with 2 papers
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In contrast, the extra $U(1)$ isometry of the solutions counted in [ref] destroys the function-dependent nature of the moduli space and makes it finite-dimensional, hence such solutions cannot be expected to have an entropy that grows with the charges in the same way as that of the most general smooth supergravity solution.
Quantizing N=2 Multicenter Solutions · Conclusions · 0.97
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In contrast, the extra $U(1)$ isometry of the solutions counted in [ref] destroys the function-dependent nature of the moduli space and makes it finite-dimensional, hence such solutions cannot be expected to have an entropy that grows with the charges in the same way as that of the most general smooth supergravity solution.
A bound on the entropy of supergravity? · Conclusions · 0.97
Cites as support 1 paper
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Indeed, as shown in Section [ref] and in [ref] , the local condition that the supergravity solution near the supertube be smooth and free of closed timelike curves is exactly the same as the condition that the supertube be a solution to the DBI action.
Supertubes in Bubbling Backgrounds: Born-Infeld Meets Supergravity · Conclusions · 0.96
Cites as background 17 papers
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where $ds_4^2$ is a four-dimensional hyper-Kähler metric [ref] [This metric can have regions of signature $+4$ and signature $-4$ [ref] , and for this reason we usually refer to it as ambipolar.].
One Ring to Rule Them All ... and in the Darkness Bind Them? · The general back-reacted solution with fluctuating electric charge densities · 0.91
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where $ds_4^2$ is a four-dimensional hyper-Kähler metric [ref] [This metric can have regions of signature $+4$ and signature $-4$ [ref] , and for this reason we usually refer to it as ambipolar.].
General Concentric Black Rings · The general back-reacted solution with fluctuating electric charge densities · 0.91
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where $ds_4^2$ is a four-dimensional hyper-Kähler metric [ref] [This metric can have regions of signature $+4$ and signature $-4$ [ref] , and for this reason we usually refer to it as ambipolar.].
Geometry of D1-D5-P bound states · The general back-reacted solution with fluctuating electric charge densities · 0.91
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