Scalar charges in asymptotic AdS geometries

We show that for n  -dimensional Einstein gravity coupled to a scalar field with mass-squared m02=−n(n−2)/(4ℓ2), the first law of thermodynamics of (charged) AdS black holes will be modified by the boundary conditions of the scalar field at asymptotic infinity. Such scalars can arise in gauged supergravities in four and six dimensions, but not in five or seven. The result provides a guiding principle for constructing designer black holes and solitons in general dimensions, where the properties of the dual field theories depend on the boundary conditions.