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Supersymmetry as a Cosmic Censor
High Energy Physics - Theory · Submitted 13 May 1992
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The supersymmetric positivity bound for dilaton black holes, $M \geq \frac{1}{\sqrt 2}(|Q|+|P|)$, takes care of the absence of naked singularities of the dilaton black holes and is, in this sense, equivalent to the cosmic censorship condition.
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The abstract, sentence by sentence
In supersymmetric theories the mass of any state is bounded below by the values of some of its charges. The corresponding bounds in case of Schwarzschild and Reissner-Nordstr\"om black holes are known to coincide with the requirement that naked singularities be absent. Here we investigate charged dilaton black holes in this context. We show that the extreme solutions saturate the supersymmetry bound of $N=4\ d=4$ supergravity, or dimensionally reduced superstring theory. Specifically, we have shown that extreme dilaton black holes, with electric and magnetic charges, admit super-covariantly constant spinors. The supersymmetric positivity bound for dilaton black holes, $M \geq \frac{1}{\sqrt 2}(|Q|+|P|)$, takes care of the absence of naked singularities of the dilaton black holes and is, in this sense, equivalent to the cosmic censorship condition. The temperature, entropy and singularity are discussed. The Euclidean action (entropy) of the extreme black hole is given by $2\pi |PQ|$. We argue that this result, as well as the one for Lorentzian signature, is not altered by higher order corrections in the supersymmetric theory. When a black hole reaches its extreme limit, it cannot continue to evaporate by emitting elementary particles, since this would violate the supersymmetric positivity bound. We speculate on the possibility that an extreme black hole may ``evaporate" by emitting smaller extreme black holes.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In supersymmetric theories the mass of any state is bounded below by the values of some of its charges. | background 1.00 | 0.07 | 0.05 | asserted 1.00 |
| s1 | The corresponding bounds in case of Schwarzschild and Reissner-Nordstr\"om black holes are known to coincide with the requirement that naked singularities be absent. | background 1.00 | 0.05 | 0.04 | asserted 1.00 |
| s2 | Here we investigate charged dilaton black holes in this context. | contribution 0.93 | 0.55 | 0.02 | unclear 0.58 |
| s3 | We show that the extreme solutions saturate the supersymmetry bound of $N=4\ d=4$ supergravity, or dimensionally reduced superstring theory. | result 0.91 | 0.89 | 0.19 | asserted 1.00 |
| s4 | Specifically, we have shown that extreme dilaton black holes, with electric and magnetic charges, admit super-covariantly constant spinors. | result 0.96 | 0.94 | 0.17 | asserted 1.00 |
| s5 | The supersymmetric positivity bound for dilaton black holes, $M \geq \frac{1}{\sqrt 2}(|Q|+|P|)$, takes care of the absence of naked singularities of the dilaton black holes and is, in this sense, equivalent to the cosmic censorship condition. | interpretation 0.61 | 0.85 | 0.83 | asserted 1.00 |
| s6 | The temperature, entropy and singularity are discussed. | contribution 0.90 | 0.62 | 0.02 | unclear 0.67 |
| s7 | The Euclidean action (entropy) of the extreme black hole is given by $2\pi |PQ|$. | result 1.00 | 0.84 | 0.08 | asserted 1.00 |
| s8 | We argue that this result, as well as the one for Lorentzian signature, is not altered by higher order corrections in the supersymmetric theory. | interpretation 0.62 | 0.55 | 0.10 | asserted 0.49 |
| s9 | When a black hole reaches its extreme limit, it cannot continue to evaporate by emitting elementary particles, since this would violate the supersymmetric positivity bound. | interpretation 0.86 | 0.49 | 0.14 | asserted 1.00 |
| s10 | We speculate on the possibility that an extreme black hole may ``evaporate" by emitting smaller extreme black holes. | future work 0.85 | 0.11 | 0.05 | speculative 1.00 |
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Original abstract
In supersymmetric theories the mass of any state is bounded below by the values of some of its charges. The corresponding bounds in case of Schwarzschild and Reissner-Nordstr\"om black holes are known to coincide with the requirement that naked singularities be absent. Here we investigate charged dilaton black holes in this context. We show that the extreme solutions saturate the supersymmetry bound of $N=4\ d=4$ supergravity, or dimensionally reduced superstring theory. Specifically, we have shown that extreme dilaton black holes, with electric and magnetic charges, admit super-covariantly constant spinors. The supersymmetric positivity bound for dilaton black holes, $M \geq \frac{1}{\sqrt 2}(|Q|+|P|)$, takes care of the absence of naked singularities of the dilaton black holes and is, in this sense, equivalent to the cosmic censorship condition. The temperature, entropy and singularity are discussed. The Euclidean action (entropy) of the extreme black hole is given by $2\pi |PQ|$. We argue that this result, as well as the one for Lorentzian signature, is not altered by higher order corrections in the supersymmetric theory. When a black hole reaches its extreme limit, it cannot continue to evaporate by emitting elementary particles, since this would violate the supersymmetric positivity bound. We speculate on the possibility that an extreme black hole may ``evaporate" by emitting smaller extreme black holes.
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References
How the literature uses it
26 arXiv papers cite this in 60 sentences
Papers citing it · 34 sentences without a confident label
Builds on it 1 paper
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The dyonic black hole solution of [ref] was found for the bosonic sector of $SO(4)$ supergravity [ref] , but since the two versions are the same at the level of equations of motion, that is also a solution to the $SU(4)$ version.
Dyonic black holes and dilaton charge in string theory · Einstein-Maxwell-dilaton theory · 0.84
Compares with it 2 papers
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In this section we show how to recover the known four parameters non-extremal and extremal black hole solutions found in [ref] by Kallosh et al. * Non-extremal dyonic black hole: In order to obtain this solution, we solve ([ref]) and ([ref]) for $r_1$ and $r_2$, by making the redefinitions $r_1≡r_-$ and $r_2≡r_+$ .
Dyonic black holes and dilaton charge in string theory · Relation to known solutions · 0.80
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In [ref] the black hole has the metric and thermodynamic properties of a Schwarzschild solution, whereas the solution found in [ref] has the metric and thermodynamic properties of a Reissner-Nordstrom black hole.
Dyonic AdS_4 black hole entropy and attractors via entropy function · Introduction · 0.98
Cites it as background 14 papers
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The Killing spinor equations can be solved to find supersymmetric black hole solutions to $=2$ supergravity coupled to vector multiplets (containing vectors, scalars and their fermionic superpartners).[Already earlier, the most general form of a supersymmetric solution had been discussed in [ref] and supersymmetric solutions were found from the supersymmetry transformations in other theories, as $= 4$ supergravity in four dimensions, see for instance [ref] .] After one makes the correct for the vector gauge fields, one obtains a set of first-order equations determining the radial flow of the scalars and warp factor of the metric.
Hidden Structures of Black Holes · First order formalisms for specific black hole solutions · 0.92
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The explicit supersymmetry analysis has been studied for stationary axion-dilaton solutions and dilaton black holes mostly in the $U(1)×U(1)$ truncated sector of $𝒩=4$ supergravity [ref] .
Supersymmetry and Attractors in N = 4 Supergravity: The Superconformal Approach · Introduction · 0.88
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Please review [ref] for more technical and structural details.] of $𝒩=4$ supergravity describing the compactified superstring theories in four spacetimes [ref] .
Logarithmic correction to black hole entropy in universal low-energy string theory models · The $U(1)^2$-charged EMD and embedded $𝒩=4$ supergravity models · 0.98
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