  We demonstrate that the solutions of three-dimensional gravity obtained by
gluing two copies of a spacetime across a junction constituted of a tensile
string are in one-to-one correspondence with the solutions of the Nambu-Goto
equation in the same spacetime up to a finite number of rigid deformations. The
non-linear Nambu-Goto equation satisfied by the average of the embedding
coordinates of the junction emerges directly from the junction conditions along
with the rigid deformations and corrections due to the tension. Therefore, the
equivalence principle generalizes non-trivially to the string. Our results are
valid both in three-dimensional flat and AdS spacetimes. In the context of
AdS$_3$/CFT$_2$ correspondence, our setup could be used to describe a class of
interfaces in the conformal field theory featuring relative time
reparametrization at the interface which encodes the solution of the Nambu-Goto
equation corresponding to the bulk junction.
