  With the advent of gravitational wave astronomy and first pictures of the
"shadow" of the central black hole of our milky way, theoretical analyses of
black holes (and compact objects mimicking them sufficiently closely) have
become more important than ever. The near future promises more and more
detailed information about the observable black holes and black hole
candidates. This information could lead to important advances on constraints on
or evidence for modifications of general relativity. More precisely, we are
studying the influence of weak teleparallel perturbations on general
relativistic vacuum spacetime geometries in spherical symmetry. We find the
most general family of spherically symmetric, static vacuum solutions of the
theory, which are candidates for describing teleparallel black holes which
emerge as perturbations to the Schwarzschild black hole. We compare our
findings to results on black hole or static, spherically symmetric solutions in
teleparallel gravity discussed in the literature, by comparing the predictions
for classical observables such as the photon sphere, the perihelion shift, the
light deflection, and the Shapiro delay. On the basis of these observables, we
demonstrate that among the solutions we found, there exist spacetime geometries
that lead to much weaker bounds on teleparallel gravity than those found
earlier. Finally, we move on to a discussion of how the teleparallel
perturbations influence the Hawking evaporation in these spacetimes.
