No, the amplitude of a gravitational wave does not fall off as the inverse square law. The inverse square law is a characteristic of the intensity or flux of radiation, such as electromagnetic radiation, which follows a decrease in intensity proportional to the square of the distance from the source.
In the case of gravitational waves, the amplitude, which represents the strength or magnitude of the wave, does not decrease with distance in the same way as electromagnetic waves. Instead, gravitational waves cause space itself to stretch and compress as they propagate, and their amplitude diminishes with distance from the source.
The fall-off of the amplitude of a gravitational wave is governed by a different law known as the inverse distance law. According to this law, the amplitude of a gravitational wave decreases linearly with distance from the source. As the wave travels through space, it gradually loses energy, resulting in a decrease in amplitude as it propagates away from its origin.
It's important to note that gravitational waves are incredibly weak compared to other types of waves, and their detection requires extremely sensitive instruments, such as the Laser Interferometer Gravitational-Wave Observatory (LIGO), to measure the tiny changes in distance caused by the passing wave.