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.

35 pages, 5 figures

References in corpus (8)

• The Confrontation between General Relativity and Experiment
• Tests of general relativity from timing the double pulsar
• Progress in Measurements of the Gravitational Bending of Radio Waves Using the VLBA
• Equivalence of the Einstein and Jordan frames
• Invariant quantities in the scalar-tensor theories of gravitation
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Testing scalar-tensor theories and PPN parameters in Earth orbit
• Post-Newtonian parameter $\gamma$ for multiscalar-tensor gravity with a general potential

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