  We show a constantly accelerated quark as a string solution of the Nambu-Goto
action, which is embedded in the bulk background dual to the $\cal{N}$ $=2$
supersymmetric confining Yang-Mills theory. The induced metric of the world
sheet for this string solution has an event horizon specified by the fifth
coordinate. By an extended Rindler transformation proposed by Xiao, we move to
the comoving frame of the accelerated quark-string. Then we find that this
horizon is transferred to the event horizon of the bulk and the causal part of
the accelerated quark is transformed to a static free-quark in the Rindler
coordinate. As a result, the confinement of the Minkowski vacuum is lost in the
Rindler vacuum. This point is assured also by studying the potential between
the quark and anti-quark. However, the remnants of the original confining force
are seen in various thermal quantities. We also discuss the consistency of our
results and the claim that the Green's functions will not be changed by the
Rindler transformation.
