The time-diffraction technique introduced by Porras recently is motivated in this article in terms of the Lorentz invariance of the equation governing the narrow angular spectrum and narrowband temporal spectrum paraxial approximation and it is used to derive finite-energy spatiotemporally confined subluminal, luminal and superluminal Airy wave packets. In addition, a novel exact finite-energy luminal Airy splash mode-type solution to the scalar wave equation is derived using Bateman's conformal transformation.