Noncommutative solitons of gravity

Asakawa, Tsuguhiko; Kobayashi, Shinpei

doi:10.1088/0264-9381/27/10/105014

Cited by 7 publications

(15 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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.

View full text Add to dashboard Cite

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.

show abstract

Section: Conclusion and Discussionmentioning

confidence: 99%

Contravariant gravity on Poisson manifolds and Einstein gravity

Kaneko¹,

Muraki²,

Watamura³

2017

Class. Quantum Grav.

View full text Add to dashboard Cite

show abstract

“…The spacetime denoted by this metric has an angular momentum that is similar to the BTZ black hole. 4 For the energy-momentum tensor T µ ν , we impose the following ansatz…”

Section: Three-dimensional Rotating Regular Black Hole With Anisotropmentioning

confidence: 99%

Regular black holes and noncommutative geometry inspired fuzzy sources

Kobayashi

2016

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…This means that the generalized Einstein field equation has been calculated which is given by (69) with (73) and thus (70) and (71) transformed to the corresponding expressions depending on the usual expansion field h µ m and (74). Accordingly generalized dynamics for the matter field coupled to gravity and for the gravitational field itself have been derived by building expectation values of the corresponding matter field equation and the Einstein field equation containing the tetrad field operatorê µ m with respect to coherent states referring to creation and annihilation operators being built from the components of the tetrad field operatorê µ m .…”

Section: Generalized Field Equation For Matter Coupled To Gravitymentioning

confidence: 99%

Canonical noncommutativity algebra for the tetrad field in general relativity

Kober

2011

Class. Quantum Grav.

View full text Add to dashboard Cite

General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the noncommutativity algebra of the coordinates in the canonical case of noncommutative geometry, this idea is closely related to noncommutative geometry as well as to canonical quantization of gravity. According to this presupposition generalized field equations for general relativity are derived which are obtained by replacing the usual tetrad field by the tetrad field operator within the actions and then building expectation values of the corresponding field equations between coherent states. These coherent states refer to creation and annihilation operators created from the components of the tetrad field operator. In this sense the obtained theory could be regarded as a kind of semiclassical approximation of a complete quantum description of gravity. The consideration presupposes a special choice of the tensor determining the algebra providing a division of space-time into two two-dimensional planes.

show abstract

Noncommutative solitons of gravity

Cited by 7 publications

References 50 publications

Contravariant gravity on Poisson manifolds and Einstein gravity

Contravariant gravity on Poisson manifolds and Einstein gravity

Regular black holes and noncommutative geometry inspired fuzzy sources

Canonical noncommutativity algebra for the tetrad field in general relativity

Contact Info

Product

Resources

About