A novel general relativistic plane-wave metric is presented with a proposal for possible detection. Called a quasi-inertial oscillation (QIO), the metric is an exact solution to Einstein's vacuum field equations, yet carries non-Einsteinian longitudinal polarization, permitted by its quasi-inertial status. Although QIOs are metric waves in spacetime, they differ fundamentally from the standard gravitational waves assumed to be detected by LIGO and Virgo. QIOs are an oscillating type of quasi-inertial disturbance (QID), a broader class of exact solutions to Einstein's equations with varying features that travel at the speed of light. The observable properties of QIDs, and of QIOs in particular, have rarely if ever been studied in the literature. Yet it is shown here that if general relativity accurately models gravity, QIOs should produce test particle acceleration and are thus in principle observable by space-based detectors. Due to Riemann flatness, QIOs were historically dismissed as unphysical, and hence unobservable, by authors such as Taub, McVittie, Weber and others. However, these authors were seeking gravitational waves capable of forming gravitons, a far more stringent requirement than mere observability. Moreover, the claim that Riemann flatness precludes detection does not apply to metrics for which the coordinate system is fixed by a physical structure, such as a space-based platform, an accelerating rocket, or the cosmic microwave background, nor to metrics associated with frame-dependent quantum processes such as the Unruh effect. Nevertheless, subsequent authors continued to dismiss exact longitudinal plane-wave solutions and thus overlooked a real possibility of detection. With the benefit of hindsight, it is proposed here that QIOs may not only be detectable, but that Riemann flatness does not rule out the potential influence of QIOs on astrophysical or cosmological backgrounds, including the stochastic gravitational wave and photon backgrounds. QIOs are presented first in rectangular coordinates, then in Brinkmann coordinates for comparison with pp-waves. It is also shown that the Riemann-flat metric of a uniformly accelerating Rindler frame, theoretically detectable by Unruh radiation, can be constructed as a product of (rectangular) advanced and retarded QIDs, offering further argument for observability through an Unruh-type effect. Astrophysical and cosmological mechanisms are proposed as physical sources of QIOs. It is further suggested that, since QIOs are energy-free exact solutions to Einstein's equations, there is nothing to obstruct their generation by accidental alignments of matter, and thus nothing to prevent the vacuum from being filled with weak transient random spacetime fluctuations.