Higher-order gravity theories admit singularity-free gravitational wave solutions

Working within quadratic and six-derivative extensions of general relativity, the authors catalogue static, spherically symmetric vacuum solutions and examine which ones support exact gravitational-wave solutions. In standard Einstein gravity, gravitational waves on the Nariai background always carry singularities interpreted as wave-generating sources. Higher-derivative theories break this rule: for specific values of their coupling constants, they admit globally smooth wave solutions with no singularity anywhere. The result sharpens the physical distinction between general relativity and its higher-derivative cousins at the level of exact solutions.