  We study a static black hole localized on a brane in the Randall-Sundrum (RS)
II braneworld scenario. To solve this problem numerically, we develop a code
having the almost 4th-order accuracy. This code derives the highly accurate
result for the case where the brane tension is zero, i.e., the spherically
symmetric case. However, a nonsystematic error is detected in the cases where
the brane tension is nonzero. This error is irremovable by any systematic
methods such as increasing the resolution, setting the outer boundary at more
distant location, or improving the convergence of the numerical relaxation. We
discuss the possible origins for the nonsystematic error, and conclude that our
result is naturally interpreted as the evidence for the nonexistence of
solutions to this setup, although an "approximate" solution exists for
sufficiently small brane tension. We discuss the possibility that the black
holes produced on a brane may be unstable and lead to two interesting
consequences: the event horizon pinch and the brane pinch.
