Approximate black holes for numerical relativity

Spherically symmetric solutions in Brans-Dicke theory of relativity with a zero coupling constant, $\omega =0\mathrm{}$, are derived in the Schwarzschild line element. The solutions are obtained from a cubic transition equation with one small parameter. The exterior space-time of one family of solutions is arbitrarily close to the exterior Schwarzschild space-time, while maintaining global regularity. These nontopological solitons are proposed as candidates for approximate black holes in numerical relativity, particularly for the treatment of horizon boundary conditions.