A new coordinate condition in general relativity

Duan, Yi‐Shi; Zhang, Shengli; Jiang, Licai

doi:10.1007/bf00756945

Cited by 8 publications

(3 citation statements)

References 7 publications

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“…With a generalized coordinate condition, given by Duan et al [14], the metric can in fact be written in spherical polar coordinates in such a way that…”

Section: The Theoremmentioning

confidence: 99%

Towards a characterization of fields leading to black hole hair

Banerjee

Sen

2015

Pramana - J Phys

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In the present work, it is shown that an asymptotically flat spherical black hole can have a nontrivial signature of any field for an exterior observer if the energy momentum tensor of the corresponding field is either tracefree or if the trace falls off at least as rapidly as inverse cube of the radial distance. In the absence of a general No Hair Theorem, this result can provide a characterization of the fields leading to black hole hair.

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“…With a generalized coordinate condition, given by Duan et al [14], the metric can in fact be written in spherical polar coordinates in such a way that…”

Section: The Theoremmentioning

confidence: 99%

Towards a characterization of fields leading to black hole hair

Banerjee

Sen

2015

Pramana - J Phys

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“…As a matter of fact, this is just the equation of harmonic map.' 22 ! In summary, we have studied the gauge theory of spacetime defects through the new topological invariant which is closely related to the torsion tensor in Riemann-Cartan manifold.…”

Section: \J(hv) Pt \ J(hv) Pi ' [ 'mentioning

confidence: 99%

The Topological Quantization and Bifurcation of Strings in Early Universe

Duan

Jiang

Gao

2000

Commun. Theor. Phys.

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We present a new topological invariant to describe the spacetime defect in Riemann–Cartan manifold. By means of the -mapping theory and the rank-two topological tensor current (associated to the new topological invariant), we show that there must exist many string objects which naturally generated from the zero points of -mapping and is quantized in the topological level under the condition that the Jacobian . When , we find that there exists a crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the origin and bifurcation of the strings are detailed in the neighborhoods of the limit points and bifurcation points of -mapping, respectively.

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“…24 Because g u is a 4 × 4 determinant, even if we consider some constraint conditions, the explicit forms of equations of motion are still complicated. It is also obvious that the equations have strong nonlinear property.…”

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confidence: 99%

Fourth-Order Topological Tensor Current and Fock's Coordinate Condition

Gao

Duan

1998

Mod. Phys. Lett. A

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From φ-mapping method we construct a fourth-order topological tensor current in general. It is shown that the inner structure of this topological tensor current is labelled by the δ-function δ(φ), which represents some four-dimensional singular manifolds. By investigating the total expansion of δ(φ), these singular manifolds carry the topological numbers β i η i naturally, which does not involve any concrete models. As the generalization of Nielsen's Lagrangian and Nambu's action for strings, we present a new coordinate condition in general relativity, which includes the Fock's coordinate condition as a special case.In nonlinear σ-models, 9 the Skyrmions currents 10 (whose charges have many properties in common with baryon numbers 11 ), the topological current of dislocation and disclination continuum, 12 the space-time defects in the early universe, 13 the GaussBonnet-Chern theorem and the topological charge of Chern class. 14 In our previous papers, 2,5,7 based on the so-called φ-mapping method, only topological current of point-like particles was discussed. In this letter we will extend the concept. We consider the φ-mapping as a map of an n-dimensional Riemann manifold X onto an (n − 4)-dimensional Euclidean space R n−4 . From this map we can construct a fourth-order topological tensor current and study its inner structure naturally. From the viewpoint of submanifold of X, four-dimensional Riemann manifolds are generated by the kernel of φ-mapping and the famous Fock's coordinate condition is naturally deduced without any concrete models.We start by introducing the so-called φ-mapping method. Let X be an ndimensional Riemann manifold with metric tensor g µν and local coordinates x µ (µ, ν = 1, . . . , n), and R n−4 a Euclidean space with dimension m = n − 4 and coordinates φ a (a = 1, . . . , m). A smooth map φ: X −→ R n−4 gives an (n − 4)-dimensional smooth vector field on X, which can be represented in the coordinate 745 Mod. Phys. Lett. A 1998.13:745-752. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ SAN DIEGO on 06/04/15. For personal use only.

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A new coordinate condition in general relativity

Cited by 8 publications

References 7 publications

Towards a characterization of fields leading to black hole hair

Towards a characterization of fields leading to black hole hair

The Topological Quantization and Bifurcation of Strings in Early Universe

Fourth-Order Topological Tensor Current and Fock's Coordinate Condition

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