No, a black hole cannot accelerate an object beyond the speed of light through its gravitational attraction. According to the theory of general relativity, the gravitational pull of a black hole becomes stronger as you get closer to it, but it does not directly cause objects to exceed the speed of light.
Within the vicinity of a black hole, the space-time curvature is extremely intense, leading to significant time dilation and warping of space. As an object approaches the event horizon (the boundary of a black hole), the gravitational force becomes increasingly powerful. However, even at the event horizon, the escape velocity required to break free from the black hole's gravitational pull is still below the speed of light.
In other words, an object falling into a black hole will never exceed the speed of light as it approaches or crosses the event horizon. Instead, it will continue to accelerate toward the speed of light but never surpass it.
It's worth noting that our current understanding of physics suggests that nothing with mass can travel at or faster than the speed of light in a vacuum. The theory of relativity sets a universal speed limit, known as the speed of light, which cannot be exceeded.