The collision between two massive black holes does not create new space or new spacetime. Instead, it causes a distortion in the existing spacetime fabric, which is a consequence of Einstein's general theory of relativity.
According to general relativity, massive objects like black holes curve the fabric of spacetime around them. This curvature determines how objects and light move in the vicinity of the black holes. When two black holes merge, their combined mass and angular momentum cause ripples in the fabric of spacetime, analogous to waves spreading out from a disturbance in water.
These ripples are known as gravitational waves. Gravitational waves are a prediction of general relativity and are created whenever there is a significant change in the distribution of mass and energy. As the black holes spiral closer to each other during their final orbits, they release a tremendous amount of energy in the form of gravitational waves.
The gravitational waves carry away energy and angular momentum from the system, causing the black holes to inspiral towards each other at an increasing rate. Eventually, they merge into a single, more massive black hole. During this process, the curvature of spacetime is rearranged, but no new spacetime or space is created.
However, it's worth noting that the merger of black holes and the resulting gravitational waves can provide us with valuable information about the nature of spacetime and the behavior of gravity. The detection of gravitational waves by advanced instruments like LIGO (Laser Interferometer Gravitational-Wave Observatory) and VIRGO has opened up a new window into the study of the universe, allowing us to observe and explore phenomena that were previously inaccessible.