Tensor gauge condition and tensor field decomposition

Chen, Xiang-Song; Zhu, Ben‐Chao

doi:10.48550/arxiv.1101.2809

Cited by 5 publications

(11 citation statements)

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“…(11) and ( 16) are exactly the same. In two other papers of this serial study [4,5], we show that such construction applies quite generally to any symmetric tensor field, and can be derived by seeking a unique decomposition of a tensor field into physical and pure-gauge components, analogous to the recent physical decomposition of the Abelian and non-Abelian gauge fields by Chen and collaborators [6,7].…”

mentioning

confidence: 79%

“…This can be seen by comparing Eqs. (1) and (5). They differ by a term ∂ 0 h ρ 0 − 1 2 ∂ ρ h 0 0 , in which ∂ ρ h 0 0 can be non-zero even for a static case.…”

mentioning

confidence: 99%

“…It must be noted, however, that ∂ i ρ i = 0 does not lead to the desired gauge (5). This might partially explain why the gauge (5) has eluded people's attention.…”

mentioning

confidence: 99%

“…( 22) that provides a pertinent metric for calculating the energy density of gravitational field [11]. More importantly, when discussing the distribution of energy flow in gravitational radiation, one should always work in the "true" radiation gauge (5), or equivalently in the TT gauge if one concerns about the radiation zone far away from the source. The latter approach was adopted in Ref.…”

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confidence: 99%

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True radiation gauge for gravity

2011

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Corresponding to the similarity between the Lorentz gauge ∂ µ A µ = 0 in electrodynamics and g µν Γ ρ µν = 0 in gravity, we show that the counterpart of the radiation gauge ∂ i A i = 0 is g ij Γ ρ ij = 0, in stead of other forms as discussed before. Particularly: 1) at least for a weak field, g ij Γ ρ ij = 0 fixes the gauge completely and picks out exactly the two physical components of the gravitational field;2) like A 0 , the non-dynamical components h 0µ are solved instantaneously; 3) gravitational radiation is generated by the "transverse" part of the energy-momentum tensor, similar to the transverse current J ⊥ . This "true" radiation gauge g ij Γ ρ ij = 0 is especially pertinent for studying gravitational energy, such as the energy flow in gravitational radiation. It agrees with the transverse-traceless (TT) gauge for a pure wave, and reveals remarkably how the TT gauge can be adapted in the presence of source.

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mentioning

confidence: 79%

“…This can be seen by comparing Eqs. (1) and (5). They differ by a term ∂ 0 h ρ 0 − 1 2 ∂ ρ h 0 0 , in which ∂ ρ h 0 0 can be non-zero even for a static case.…”

mentioning

confidence: 99%

“…It must be noted, however, that ∂ i ρ i = 0 does not lead to the desired gauge (5). This might partially explain why the gauge (5) has eluded people's attention.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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True radiation gauge for gravity

2011

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“…The relations between our decomposition and that of ADM and York, especially beyond the linear order, will be further explored elsewhere. [12] This work is supported by the China NSF Grants 10875082 and 11035003. XSC is also supported by the NCET Program of the China Education Department.…”

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confidence: 99%

Physical decomposition of the gauge and gravitational fields

Chen

Zhu

2011

Phys. Rev. D

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Physical decomposition of the non-Abelian gauge field has recently solved the two-decade-lasting problem of a meaningful gluon spin. Here we extend this approach to gravity and attack the century-lasting problem of a meaningful gravitational energy. The metric is unambiguously separated into a pure geometric term which contributes null curvature tensor, and a physical term which represents the true gravitational effect and always vanishes in a flat space-time. By this decomposition the conventional pseudo-tensors of the gravitational stress-energy are easily rescued to produce definite physical result. Our decomposition applies to any symmetric tensor, and has interesting relation to the transverse-traceless (TT) decomposition discussed by Arnowitt, Deser and Misner, and by York.Comment: 11 pages, no figure; significant revision, with discussion on relations of various metric decomposition

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Dynamical Hamilton Density of Gravitational Field

Zhu¹,

Zhang²,

Jiang³

et al. 2016

Proceedings of the 6th International Conference on Electronic, Mechanical, Information and Management Society

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Abstract. Following the recent study about "general transverse gauge condition" for gravity in weak field approximation in Ref [5], we revisit the energy density gauge-dependent problem of gravitational field by canonical field theory procedure in this paper. Firstly, we proof the general transverse gauge condition is meaningful and operational. Then by using the general transverse gauge condition, we can get the gauge-invariant solution of Einstein equation of general relativity. The final total Hamilton density of gravitational field obtained by our procedure shows some interesting properties: i) it is absolutely gauge-invariant and thus has no gauge-dependent problem. ii) It can be divided into two parts, pure dynamical and pure instantaneous. Just like what we had known the electromagnetic energy density in electrodynamics. iii) It differs from the traditional effective stress-energy tensor 00 1 2 hh , which may contribute some energy in total radiation system.

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Tensor gauge condition and tensor field decomposition

Cited by 5 publications

References 11 publications

True radiation gauge for gravity

True radiation gauge for gravity

Physical decomposition of the gauge and gravitational fields

Dynamical Hamilton Density of Gravitational Field

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