While the absence of air resistance in space would eliminate one source of damping, there are other factors that would cause the string to eventually stop vibrating. These include:
1. Internal damping: The string itself is not perfectly elastic and will lose energy due to internal friction as it vibrates. This energy loss would cause the vibrations to gradually decay over time.
2. Radiation damping: In space, the string would emit thermal radiation, which carries energy away from the system. This would also contribute to the decay of the vibrations.
3. Contact with the guitar body: Even in space, the string would still be in contact with the guitar body, which would provide a pathway for energy to be transferred away from the string. This contact would also contribute to damping the vibrations.
Therefore, while a guitar string would vibrate for a longer period of time in space compared to on Earth, it would not vibrate forever. The vibrations would eventually decay due to internal damping, radiation damping, and contact with the guitar body.