In the scenario you described, where an observer stationary with respect to a black hole observes an object slowing to a standstill as it falls toward the event horizon, the apparent time dilation is primarily due to the gravitational field of the black hole rather than the object's velocity.
According to general relativity, the presence of a massive object, such as a black hole, causes a curvature of spacetime in its vicinity. This curvature affects the motion of objects and the flow of time. As an object approaches the intense gravitational field near the event horizon of a black hole, it experiences a significant gravitational time dilation.
The observed slowing down of the falling object is a result of the gravitational time dilation caused by the strong gravitational field of the black hole. The closer the object gets to the event horizon, the stronger the gravitational field becomes, and the more time dilation occurs. From the perspective of an observer outside the black hole, time appears to slow down for the falling object as it approaches the event horizon.
While the velocity of the object does play a role in the overall time dilation effect, it is secondary to the gravitational time dilation. In this case, the gravitational field dominates the time dilation experienced by the object.
It's important to note that the concept of time dilation near black holes can be quite complex, involving both gravitational and velocity-related effects. The exact calculations and understanding of such phenomena require detailed knowledge of general relativity and its mathematical formulations.