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 vector and scalar-like deformation, complicating efforts to use detection of such modes as evidence for modified gravity. We demonstrate that EGWs are present and dominant in the vicinity of sub-wavelength sources such as orbiting binaries.
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