When neutron stars collide, gravitational waves are produced due to the extreme acceleration and deformation of spacetime caused by the violent merger. Gravitational waves are ripples in the fabric of spacetime that propagate outward at the speed of light. They are generated by any accelerating mass, not just changes in the total amount of mass.
During a neutron star collision, the individual neutron stars are highly compact and massive objects. As they approach each other and eventually merge, they undergo rapid changes in their gravitational fields, which leads to the generation of gravitational waves. These waves carry energy away from the system in the form of gravitational radiation.
While the total amount of mass remains constant in the system, the distribution of mass changes significantly during the collision. The intense gravitational forces cause the neutron stars to deform and redistribute their mass as they merge. This redistribution of mass, coupled with the strong acceleration and changes in the gravitational field, produces gravitational waves.
Gravitational waves carry away energy and momentum from the system, resulting in the loss of mass-energy in the form of gravitational radiation. This loss of energy is responsible for the inspiral and eventual merger of the neutron stars. The emitted gravitational waves can be detected and measured using sensitive instruments like interferometers, such as the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Virgo detector.
So, although the total amount of mass in the system remains the same, the changes in mass distribution and the acceleration of the masses during a neutron star collision generate gravitational waves, allowing us to observe and study these fascinating astrophysical events.