  According to the no-hair theorem, static black holes are described by a
Schwarzschild spacetime provided there are no other sources of the
gravitational field. This requirement, however, is in astrophysical realistic
scenarios often violated, e.g., if the black hole is part of a binary system or
if it is surrounded by an accretion disk. In these cases, the black hole is
distorted due to tidal forces. Nonetheless, the subsequent formulation of the
no-hair theorem holds: The contribution of the distorted black hole to the
multipole moments that describe the gravitational field close to infinity and,
thus, all sources is that of a Schwarzschild black hole. It still has no hair.
This implies that there is no multipole moment induced in the black hole and
that its second Love numbers, which measure some aspects of the distortion,
vanish as was already shown in approximations to general relativity. But here
we prove this property for astrophysical relevant black holes in full general
relativity.
