Second post-Newtonian approximation of scalar-tensor theory of gravity

Peng Dong; Tian-Yi Huang; Wei-Tou Ni; Yi Xie

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Second post-Newtonian approximation of scalar-tensor theory of gravity

Yi Xie, Wei-Tou Ni, Peng Dong, Tian-Yi Huang

General Relativity and Quantum Cosmology · Submitted 23 Apr 2007

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The authors' main claim Here we present the full second post-Newtonian approximation of the scalar-tensor theory including viable examples of intermediate-range gravity.

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arXiv ID0704.2991 (version 3)

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CitationPeng Dong, Tian-Yi Huang, Wei-Tou Ni, Yi Xie. "Second post-Newtonian approximation of scalar-tensor theory of gravity." arXiv:0704.2991 (2007). https://pith.science/paper/QYX3YROI

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What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.45 · compares with prior results 0.35 · mentions code or data availability 0.02.

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Deep space laser ranging missions like ASTROD I (Single-Spacecraft Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD, together with astrometry missions like GAIA and LATOR will be able to test relativistic gravity to an unprecedented level of accuracy. More precisely, these missions will enable us to test relativistic gravity to $10^{-7}-10^{-9}$, and will require 2nd post-Newtonian approximation of relevant theories of gravity. The first post-Newtonian approximation is valid to $10^{-6}$ and the second post-Newtonian is valid to $10^{-12}$ in the solar system. The scalar-tensor theory is widely discussed and used in tests of relativistic gravity, especially after the interests in inflation, cosmological constant and dark energy in cosmology. In the Lagrangian, intermediate-range gravity term has a similar form as cosmological term. Here we present the full second post-Newtonian approximation of the scalar-tensor theory including viable examples of intermediate-range gravity. We use Chandrasekhar's approach to derive the metric coefficients and the equation of the hydrodynamics governing a perfect fluid in the 2nd post-Newtonian approximation in scalar-tensor theory; all terms inclusive of $O(c^{-4})$ are retained consistently in the equation of motion.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Deep space laser ranging missions like ASTROD I (Single-Spacecraft Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD, together with astrometry missions like GAIA and LATOR will be able to test relativistic gravity to an unprecedented level of accuracy.	background 1.00	0.05	0.04	hedged possibility 0.78
s1	More precisely, these missions will enable us to test relativistic gravity to $10^{-7}-10^{-9}$, and will require 2nd post-Newtonian approximation of relevant theories of gravity.	background 0.86	0.07	0.11	asserted 0.84
s2	The first post-Newtonian approximation is valid to $10^{-6}$ and the second post-Newtonian is valid to $10^{-12}$ in the solar system.	background 0.98	0.12	0.07	asserted 1.00
s3	The scalar-tensor theory is widely discussed and used in tests of relativistic gravity, especially after the interests in inflation, cosmological constant and dark energy in cosmology.	background 1.00	0.04	0.03	asserted 1.00
s4	In the Lagrangian, intermediate-range gravity term has a similar form as cosmological term.	background 0.95	0.11	0.04	asserted 1.00
s5	Here we present the full second post-Newtonian approximation of the scalar-tensor theory including viable examples of intermediate-range gravity.	contribution 1.00	0.94	0.60	asserted 1.00
s6	We use Chandrasekhar's approach to derive the metric coefficients and the equation of the hydrodynamics governing a perfect fluid in the 2nd post-Newtonian approximation in scalar-tensor theory; all terms inclusive of $O(c^{-4})$ are retained consistently in the equation of motion.	method 0.97	0.96	0.19	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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The paper

Original abstract

Deep space laser ranging missions like ASTROD I (Single-Spacecraft Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD, together with astrometry missions like GAIA and LATOR will be able to test relativistic gravity to an unprecedented level of accuracy. More precisely, these missions will enable us to test relativistic gravity to $10^{-7}-10^{-9}$, and will require 2nd post-Newtonian approximation of relevant theories of gravity. The first post-Newtonian approximation is valid to $10^{-6}$ and the second post-Newtonian is valid to $10^{-12}$ in the solar system. The scalar-tensor theory is widely discussed and used in tests of relativistic gravity, especially after the interests in inflation, cosmological constant and dark energy in cosmology. In the Lagrangian, intermediate-range gravity term has a similar form as cosmological term. Here we present the full second post-Newtonian approximation of the scalar-tensor theory including viable examples of intermediate-range gravity. We use Chandrasekhar's approach to derive the metric coefficients and the equation of the hydrodynamics governing a perfect fluid in the 2nd post-Newtonian approximation in scalar-tensor theory; all terms inclusive of $O(c^{-4})$ are retained consistently in the equation of motion.

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10 arXiv papers cite this in 14 sentences

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Papers citing it · 6 sentences without a confident label

Uses its data or values 1 paper

Note that $U$ is given by [equation] and the parameters $γ̅$, $β̅$, $ξ_1$ and $Λ$ are given in [ref] by [equation]

Light deflection in the second post-Newtonian approximation of scalar-tensor theory of gravity · Metric coefficients · 0.81

Compares with it 1 paper

Meanwhile, a 2PPN parameter in ae-theory, $ι$, which is a non-GR parameter in the 2PN $g_00$, is discussed and compared with other theories, such as a multiscalar-tensor theory [ref] and a scalar-tensor theory with an intermediate range force [ref] .

Second post-Newtonian approximation of Einstein-aether theory · Conclusions · 1.00

Cites it as background 6 papers

The full equations up to the second post-Newtonian approximation for generic $ω(Ψ)$ and $V(Ψ)$ have been worked out in Ref. [ref] , while Ref. [ref] tackles light propagation up to the same PPN order for STG with a vanishing potential.

Post-Newtonian parameters gamma and beta of scalar-tensor gravity with a general potential · Introduction · 0.93
The 2PN metric and equations of motion were computed for bodies composed of perfect fluids in Ref. [ref] .

Gravitational waveforms in scalar-tensor gravity at 2PN relative order · Introduction · 0.90
In addition, the metric sufficient to study light deflection at 2 PN order was examined in [ref] , while the generic structure of the 2 PN Lagrangian for TMST and $N$ compact bodies was derived in [ref] .

Tensor-Multi-Scalar Gravity: Equations of Motion to 2.5 post-Newtonian Order · INTRODUCTION · 0.92

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