In the context of cosmology, you can perturb around the FRW background, conventionally:$$g = a^2(\tau)[(1+2A)d\tau^2 - 2B_a dx^a d\tau -(\delta_{ab} + h_{ab}) dx^a dx^b]$$with ##a,b## being spatial indices only (1,2,3). You can do gauge transformations ##\tilde{x} = x + \xi## of the coordinates...