Scalarized Black Holes in Teleparallel Gravity

Black holes play a crucial role in the understanding of the gravitational interaction. Through the
direct observation of the shadow of a black hole by the event horizon telescope and the detection of
gravitational waves of merging black holes we now start to have direct access to their properties and
behaviour, which means the properties and behaviour of gravity. This further raised the demand
for models to compare with those observations. In this respect, an important question regarding
black holes properties is to know if they can support 'hairs'. While this is famously forbidden
in general relativity, in particular for scalar fields, by the so-called no-hair theorems, hairy black
holes have been shown to exist in several class of scalar-tensor theories of gravity. In this article
we investigate the existence of scalarized black holes in scalar-torsion theories of gravity. On one
hand, we find exact solutions for certain choices of couplings between a scalar field and the torsion
tensor of a teleparallel connection and certain scalar field potentials, and thus proof the existence of
scalarized black holes in these theories. On the other hand, we show that it is possible to establish
no-scalar-hair theorems similar to what is known in general relativity for other choices of these
functions.