1 Structure and Stability of Coldscalar - Tensor Black

We study the structure and stability of the recently discussed spherically symmetric Brans-Dicke black-hole type solutions with an innnite horizon area and zero Hawking temperature , existing for negative values of the coupling constant !. These solutions split into two classes: B1, whose horizon is reached by an infalling particle in a nite proper time, and B2, for which this proper time is innnite. Class B1 metrics are shown to be extendable beyond the horizon only for discrete values of mass and scalar charge, depending on two integers m and n. In the case of even m ? n the space-time is globally regular; for odd m the metric changes its signature at the horizon. All spherically symmetric solutions of the Brans-Dicke theory with ! < ?3=2 are shown to be linearly stable against spherically symmetric perturbations. This result extends to the generic case of the Bergmann-Wagoner class of scalar-tensor theories of gravity with the coupling function !() < ?3=2.