  A certain vector-tensor (VT) theory of gravitation was tested in previous
papers. In the background universe, the vector field of the theory has a
certain energy density, which is appropriate to play the role of vacuum energy
(cosmological constant). Moreover, this background and its perturbations may
explain the temperature angular power spectrum of the cosmic microwave
background (CMB) obtained with WMAP (Wilkinson Map Anisotropy Probe), and other
observations, as e.g., the Ia supernova luminosities. The parametrized
post-Newtonian limit of the VT theory has been proved to be identical to that
of general relativity (GR), and there are no quantum ghosts and classical
instabilities. Here, the stationary spherically symmetric solution, in the
absence of any matter content, is derived and studied. The metric of this
solution is formally identical to that of the Reissner-Nordstr\"om-de Sitter
solution of GR, but the role of the electrical charge is played by a certain
quantity $\Gamma $ depending on both the vector field and the parameters of the
VT theory. The black hole and cosmological horizons are discussed. The radius
of the VT black hole horizon deviates with respect to that of the
Kottler-Schwarzschild-de Sitter radius. Realistic relative deviations depend on
$\Gamma $ and reach maximum values close to 30 per cent. For large enough
$\Gamma $ values, there is no any black hole horizon, but only a cosmological
horizon. The radius of this last horizon is almost independent of the mass
source, the vector field components, and the VT parameters. It essentially
depends on the cosmological constant value, which has been fixed by using
cosmological observational data (CMB anisotropy, galaxy correlations and so
on).
