  We develop an effective framework for the $\bar\mu$ scheme of holonomy
corrections motivated by loop quantum gravity for vacuum spherically symmetric
space-times. This is done by imposing the areal gauge in the classical theory,
and then expressing the remaining components of the Ashtekar-Barbero connection
in the Hamiltonian constraint in terms of holonomies of physical length
$\ell_{\rm Pl}$. The stationary solutions to the effective Hamiltonian
constraint can be found exactly, and we give the explicit form of the effective
metric in Painlev\'e-Gullstrand coordinates. This solution has the correct
classical limit, the quantum gravity corrections decay rapidly at large
distances, and curvature scalars are bounded by the Planck scale, independently
of the black hole mass $M$. In addition, the solution is valid for radii $x \ge
x_{\rm min} \sim (\ell_{\rm Pl}^2 M)^{1/3}$ indicating the need for a matter
field, with an energy density bounded by the Planck scale, to provide a source
for the curvature in the space-time. Finally, for $M \gg m_{\rm Pl}$, the
space-time has an outer and also an inner horizon, within which the expansion
for outgoing radial null geodesics becomes positive again. On the other hand,
for sufficiently small $M \sim m_{\rm Pl}$, there are no horizons at all in the
effective metric.
