We describe the properties of evanescent gravitational waves (EGWs)---wave solutions of Einstein equations which decay exponentially in some direction while propagating in another. Evanescent waves are well-known in acoustics and optics and have recently received much attention due to their extraordinary properties such as their transverse spin and spin-momentum locking. We show that EGWs possess similarly remarkable properties, carrying transverse spin angular momenta and driving freely falling test masses along in elliptical trajectories. Hence, test masses on a plane transverse to the direction of propagation exhibit correlated vector and scalar-like deformation---correlations which can be used to distinguish it from modified gravity. We demonstrate that EGWs are present and dominant in the vicinity of sub-wavelength sources such as orbiting binaries.

13 pages, movie link https://youtu.be/DB7mHGqsrLk