  The effect of the Hawking temperature on the entanglement and teleportation
for the scalar field in a most general, static and asymptotically flat black
hole with spherical symmetry has been investigated. It is shown that the same
"initial entanglement" for the state parameter $\alpha$ and its "normalized
partners" $\sqrt{1-\alpha^{2}}$ will be degraded by the Hawking effect with
increasing Hawking temperature along two different trajectories except for the
maximally entangled state. In the infinite Hawking temperature limit,
corresponding to the case of the black hole evaporating completely, the state
has no longer distillable entanglement for any $\alpha$. It is interesting to
note that the mutual information in this limit equals to just half of the
"initially mutual information". It has also been demonstrated that the fidelity
of teleportation decreases as the Hawking temperature increases, which just
indicates the degradation of entanglement.
