The phenomenon of time dilation near a black hole does indeed cause time to appear to slow down for an outside observer. However, this does not mean that events themselves appear to slow down or become frozen from the perspective of an observer outside the black hole.
When two black holes collide and emit gravitational waves, these waves propagate through spacetime at the speed of light. As they travel, the gravitational waves carry information about the motion and properties of the merging black holes. While time may be perceived to slow down near a black hole, the gravitational waves themselves are not subject to the same time dilation effects.
From our perspective, we can detect the gravitational waves emitted by the colliding black holes using specialized detectors like LIGO (Laser Interferometer Gravitational-Wave Observatory). These detectors are designed to measure tiny changes in the length of their arms caused by passing gravitational waves.
The gravitational waves emitted by the colliding black holes will be detected as a series of oscillations in the LIGO detectors. These oscillations represent the inspiral, merger, and ringdown phases of the black hole collision. Although time may appear to slow down near the black holes, the emitted gravitational waves still carry information about the entire process, including the merger itself.
So, even though time dilation near a black hole affects our perception of time, it does not prevent us from observing and detecting the gravitational waves emitted by colliding black holes. We can still witness the inspiral, merger, and the aftermath of black hole collisions through the gravitational wave signals they generate.