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The structure of neutron stars is investigated in the context of a scalar-tensor theory of gravity with variable Brans-Dicke parameter omega(phi). Neutron star models are constructed using the Pandharipande (hyperon) equation of state and an equation of state that maximizes the mass for various values of a variability parameter alpha. It is shown that the neutron stars are more compact and less massive than their counterparts in general relativity and standard Brans-Dicke theory. The compactness of an astrophysical body is generally measured by its sensitivity to changes in the gravitational constant and is important in the analysis of the orbital motion in close binary systems. This paper gives a more general definition for this sensitivity in a general scalar-tensor theory, and dependence on alpha is calculated. The effects can be quite significant even for omega greater than 500 and alpha within the experimental bounds, and can therefore provide a window for testing scalar-tensor theories of gravity that are indistinguishable from general relativity in the solar system.
Helmut W. Zaglauer (Wed,) studied this question.