Post-Newtonian parameters $\gamma$ and $\beta$ of scalar-tensor gravity for a homogeneous gravitating sphere

Abstract

We calculate the parameters $\gamma$ and $\beta$ in the parametrized post-Newtonian (PPN) formalism for scalar-tensor gravity (STG) with an arbitrary potential, under the assumption that the source matter is given by a non-rotating sphere of constant density, pressure and internal energy. For our calculation we write the STG field equations in a form which is manifestly invariant under conformal transformations of the metric and redefinitions of the scalar field. This easily shows that also the obtained PPN parameters are invariant under such transformations. Our result is consistent with the expectation that STG is a fully conservative theory, i.e., only $\gamma$ and $\beta$ differ from their general relativity values $\gamma =\beta =1$, which indicates the absence of preferred frame and preferred location effects. We find that the values of the PPN parameters depend on both the radius of the gravitating mass source and the distance between the source and the observer. Most interestingly, we find that also at large distances from the source $\beta$ does not approach $\beta =1$, but receives corrections due to a modified gravitational self-energy of the source. Finally, we compare our result to a number of measurements of $\gamma$ and $\beta$ in the Solar System. We find that in particular measurements of $\beta$ improve the previously obtained bounds on the theory parameters, due to the aforementioned long-distance corrections.

arXiv comment35 pages, 5 figures

References in corpus (29)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Planck 2015 results. XIII. Cosmological parameters
• The Confrontation between General Relativity and Experiment
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• The String Dilaton and a Least Coupling Principle
• Quintessence and the Rest of the World
• Tests of general relativity from timing the double pulsar
• Evidence for the spin-0 nature of the Higgs boson using ATLAS data
• Post-Newtonian constraints on f(R) cosmologies in metric formalism
• Post-Newtonian constraints on f(R) cosmologies in Palatini formalism
• The conformal frame freedom in theories of gravitation
• The gravity lagrangian according to solar system experiments
• Testing the No-Hair Theorem with Event Horizon Telescope Observations of Sagittarius A*
• BlackHoleCam: fundamental physics of the Galactic center
• Progress in Measurements of the Gravitational Bending of Radio Waves Using the VLBA
• Equivalence of the Einstein and Jordan frames
• PPN Parameter $\gamma$ and Solar System Constraints of Massive Brans-Dicke Theories
• Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity
• Invariant quantities in the scalar-tensor theories of gravitation
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• A frame independent classification of single field inflationary models
• Post-Newtonian parameters gamma and beta of scalar-tensor gravity with a general potential
• Parameterized post-Newtonian limit of Horndeski's gravity theory
• Testing scalar-tensor theories and PPN parameters in Earth orbit
• Post-Newtonian parameters and cosmological constant of screened modified gravity
• Invariant quantities in the multiscalar-tensor theories of gravitation
• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential
• Solar System Constraints on Scalar Tensor Theories with Non-Standard Action
• Post-Newtonian parameter $\gamma$ and the deflection of light in ghost-free massive bimetric gravity

Cited by in corpus (14)

• Post-Newtonian limit of generalized symmetric teleparallel gravity
• Frame-invariant approach to higher-dimensional scalar-tensor gravity
• Post-Newtonian limit of generalized scalar-torsion theories of gravity
• Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories
• Unified dark sectors in scalar-torsion theories of gravity
• Pressure effects in the weak-field limit of f(R) = R + alpha R^2 gravity
• Parametrized post-Newtonian limit of generalized scalar-nonmetricity theories of gravity
• Imprints of screened dark energy on nonlocal quantum correlations
• Screening fifth forces in scalar-vector-tensor theories
• Post-Newtonian limit of generalized scalar-teleparallel theories of gravity
• Post-Newtonian Constraints on Scalar-Tensor Gravity
• Discrimination of metric theories
• A viable relativistic scalar theory of gravitation
• Parameterized Post-Newtonian Analysis of Quadratic Gravity and Solar System Constraints