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

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.

20 pages, COSPAR2006 H0.1-1

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• The Laser Astrometric Test of Relativity (LATOR) Mission
• The Laser Astrometric Test of Relativity Mission
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• ASTROD, ASTROD I and their gravitational-wave sensitivities
• Constraint on intermediate-range gravity from earth-satellite and lunar orbiter measurements, and lunar laser ranging

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• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
• Constraints on non-Newtonian gravity and axionlike particles from measuring the Casimir force in nanometer separation range
• Scalar-tensor propagation of light in the inner solar system at the millimetric level
• Tensor-Multi-Scalar Gravity: Equations of Motion to 2.5 post-Newtonian Order
• Second-order weak lensing from modified gravity
• Might the 2PN perihelion precession of Mercury become measurable in the next future?
• Parameterized second post-Newtonian framework with conservation Laws
• Light deflection in the second post-Newtonian approximation of scalar-tensor theory of gravity
• Deep-space laser-ranging missions ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) and ASTROD I for astrodynamics and astrometry