| Summary: | We compute families of spherically symmetric neutron-star models in two-derivative scalar-tensor theories of gravity with a massive scalar field. The numerical approach we present allows us to compute the resulting spacetimes out to infinite radius using a relaxation algorithm on a compactified grid. We discuss the structure of the weakly and strongly scalarized branches of neutron-star models thus obtained and their dependence on the linear and quadratic coupling parameters <inline-formula><math display="inline"><semantics><msub><mi>α</mi><mn>0</mn></msub></semantics></math></inline-formula>, <inline-formula><math display="inline"><semantics><msub><mi>β</mi><mn>0</mn></msub></semantics></math></inline-formula> between the scalar and tensor sectors of the theory, as well as the scalar mass <inline-formula><math display="inline"><semantics><mi>μ</mi></semantics></math></inline-formula>. For highly negative values of <inline-formula><math display="inline"><semantics><msub><mi>β</mi><mn>0</mn></msub></semantics></math></inline-formula>, we encounter configurations resembling a “gravitational atom”, consisting of a highly compact baryon star surrounded by a scalar cloud. A stability analysis based on binding-energy calculations suggests that these configurations are unstable and we expect them to migrate to models with radially decreasing baryon density and scalar field strength.
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