In general relativity, gravitational waves cannot travel faster than the speed of light. They do not exist in the Newtonian theory of gravitation, in which physical interactions propagate at infinite speed.
Although gravitational radiation has not been directly detected, there is indirect evidence for its existence. For example, the 1993 Nobel Prize in Physics was awarded for measurements of the Hulse-Taylorbinary star system that suggests gravitational waves are more than mathematical anomalies. Various gravitational wave detectors exist. However, they have not yet detected the phenomena.