  We study spherical charged black holes in the presence of a cosmological
constant with corrections motivated by the theory of loop quantum gravity. The
effective theory is constructed at the Hamiltonian level by introducing certain
correction terms under the condition that the modified constraints form a
closed algebra. The corresponding metric tensor is then carefully constructed
ensuring that the covariance of the theory is respected, that is, in such a way
that different gauge choices on phase space simply correspond to different
charts of the same spacetime solution. The resulting geometry is characterized
by four parameters: the three usual ones that appear in the general
relativistic limit (describing the mass, the charge, and the cosmological
constant), as well as a polymerization parameter, which encodes the
quantum-gravity corrections. Contrary to general relativity, where this family
of solutions is generically singular, in this effective model the presence of
the singularity depends on the values of the parameters. The specific ranges of
values that define the family of singularity-free spacetimes are explicitly
found, and their global structure is analyzed. In particular, the mass and the
cosmological constant need to be nonnegative to provide a nonsingular geometry,
while there can only be a bounded, relatively small, amount of charge. These
conditions are suited for any known spherical astrophysical black hole in the
de Sitter cosmological background, and thus this model provides a globally
regular description for them.
