  Utilising the master equation with source for perturbations of the
Schwarzschild-Tangherlini solution, we construct perturbative solutions
representing a black hole accelerated by a string in higher dimensions. We show
that such solutions can be uniquely determined by a single function
representing the local tension of the string, under natural asymptotic and
regularity conditions. We further study whether we can construct a localised
braneworld black hole solution from such a solution by cutting off a region
containing the string by a hypersurface and putting a vacuum brane on the
boundary. We find that the solution corresponding to the string with constant
tension does not allow such brane configuration when the bulk spacetime
dimension is greater than four, in contrast to the four dimensional case.
Further, we show that there exist infinitely many localised braneworld black
hole solutions in the perturbative sense for four-dimensional bulk spacetime,
if we allow non-uniform string tensions.
