Instability of an ‘‘approximate black hole’’

We investigate the stability of a family of spherically symmetric static solutions in vacuum Brans-Dicke theory ~with v50) recently described by van Putten. Using linear perturbation theory, we find one exponentially growing mode for every member of the family of solutions, and thus conclude that the solutions are not stable. Using a previously constructed code for spherically symmetric Brans-Dicke theory, additional evidence for instability is provided by directly evolving the static solutions with perturbations. The full nonlinear evolutions also suggest that the solutions are black-hole-threshold critical solutions. @S0556-2821~97!00810-2#