  We explore opportunities for multi-messenger astronomy using gravitational
waves (GWs) and prompt, transient low-frequency radio emission to study highly
energetic astrophysical events. We review the literature on possible sources of
correlated emission of gravitational waves and radio transients, highlighting
proposed mechanisms that lead to a short-duration, high-flux radio pulse
originating from the merger of two neutron stars or from a superconducting
cosmic string cusp. We discuss the detection prospects for each of these
mechanisms by low-frequency dipole array instruments such as LWA1, LOFAR and
MWA. We find that a broad range of models may be tested by searching for radio
pulses that, when de-dispersed, are temporally and spatially coincident with a
LIGO/Virgo GW trigger within a $\usim 30$ second time window and $\usim 200
\mendash 500 \punits{deg}^{2}$ sky region. We consider various possible
observing strategies and discuss their advantages and disadvantages. Uniquely,
for low-frequency radio arrays, dispersion can delay the radio pulse until
after low-latency GW data analysis has identified and reported an event
candidate, enabling a \emph{prompt} radio signal to be captured by a
deliberately targeted beam. If neutron star mergers do have detectable prompt
radio emissions, a coincident search with the GW detector network and
low-frequency radio arrays could increase the LIGO/Virgo effective search
volume by up to a factor of $\usim 2$. For some models, we also map the
parameter space that may be constrained by non-detections.
