Angles in fuzzy disc and angular noncommutative solitons

Kobayashi, Shinpei; Asakawa, Tsuguhiko

doi:10.1007/jhep04(2013)145

Cited by 3 publications

(6 citation statements)

References 31 publications

(77 reference statements)

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“…It would also be natural to ask whether one can move on to noncommutative spaces, applying the quantization of the Poisson structure in [19]. In this sense, as we mentioned in the introduction, our theory may be related to gravity theories on noncommutative spaces discussed in the purely mathematical as well as in the string/Mtheoretical literature, such as [3,4,[9][10][11][12][20][21][22][23][24].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Contravariant gravity on Poisson manifolds and Einstein gravity

Kaneko¹,

Muraki²,

Watamura³

2017

Class. Quantum Grav.

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A relation between gravity on Poisson manifolds proposed in [1] and Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein-Hilbert-type action yields an equation of motion which is written in terms of the analog of the Einstein tensor, and it includes couplings between the metric and the Poisson tensor. The study of the Weyl transformation reveals properties of those interactions. It is argued that this theory can have an equivalent description as a system of Einstein gravity coupled to matter. As an example, it is shown that the contravariant gravity on a two-dimensional Poisson manifold can be described by a real scalar field coupled to the metric in a specific manner.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Contravariant gravity on Poisson manifolds and Einstein gravity

Kaneko¹,

Muraki²,

Watamura³

2017

Class. Quantum Grav.

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“…As for a void, we want to state that it might be interesting to consider a source whose density distribution has the same profile as the fuzzy annulus we found in [29,33]. The density distribution of the fuzzy annulus can be written by the linear combination of arbitrary number of the generalized Gaussian functions.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The analysis so far can be applied to other type of sources inspired from noncommutative geometry in three dimensions. In [29], we considered the fuzzy disc, which is a disc-shaped region in a two-dimensional Moyal plane [30,31,32]. A Moyal plane is a flat space defined by noncommutative coordinates satisfying the commutation relation [x, y] = iθ.…”

Section: )mentioning

confidence: 99%

“…This function is roughly a radial step function that picks up a disc-shaped region around the origin r = 0 with radius R = √ 2N θ. On more details of how to find the corresponding function to an operator, one can find in [29].…”

Section: )mentioning

confidence: 99%

Section: Fuzzy Disc As a Source Of A Three-dimensional Black Holementioning

confidence: 99%

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Regular black holes and noncommutative geometry inspired fuzzy sources

Kobayashi

2016

Int. J. Mod. Phys. A

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We investigated regular black holes with fuzzy sources in three and four dimensions. The density distributions of such fuzzy sources are inspired by noncommutative geometry and given by Gaussian or generalized Gaussian functions. We utilized mass functions to give a physical interpretation of the horizon formation condition for the black holes. In particular, we investigated three-dimensional BTZ-like black holes and four-dimensional Schwarzschild-like black holes in detail, and found that the number of horizons is related to the space-time dimensions, and the existence of a void in the vicinity of the center of the space-time is significant, rather than noncommutativity. As an application, we considered a three-dimensional black hole with the fuzzy disc which is a disc-shaped region known in the context of noncommutative geometry as a source. We also analyzed a four-dimensional black hole with a source whose density distribution is an extension of the fuzzy disc, and investigated the horizon formation condition for it.

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