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The impending era of wide-field radio surveys has the potential torevolutionize our understanding of astrophysical transients. Here we evaluatethe prospects of a wide range of planned and hypothetical radio surveys usingthe properties and volumetric rates of known and hypothetical classes ofextragalactic synchrotron radio transients (e.g., on- and off-axis gamma-raybursts [GRB], supernovae, tidal disruption events [TDE], compact objectmergers). Utilizing these sources and physically motivated considerations weassess the allowed phase-space of radio luminosity and peak timescale forextragalactic transients. We also include for the first time effects such asredshift evolution of the rates, K-corrections, and non-Euclidean luminositydistance, which affect the detection rates of the most sensitive surveys. Thenumber of detected events is calculated by means of a Monte Carlo method, usingthe various survey properties (depth, cadence, area) and realistic detectioncriteria that include a cut on the minimum variability of the transients duringthe survey and an assessment of host galaxy contamination. Near-term GHzfrequency surveys (ASKAP/VAST, Very Large Array Sky Survey) will detect fewevents: <~30-50 on- and off-axis long GRBs and off-axis tidal disruptionevents, and ~10-20 neutron star binary mergers if ~1% of the mergers result ina stable millisecond magnetar. Low-frequency surveys (e.g., LOFAR) are unlikelyto detect any transients, while a hypothetical large-scale mm survey may detect~40 on-axis long GRBs. On the other hand, SKA surveys at ~0.1-1 GHz have thepotential to uncover thousands of transients, mainly on- and off-axis longGRBs, on-axis short GRBs, off-axis TDEs, and neutron star binary mergers withmagnetar remnants.

Extragalactic Transients in the Era of Wide-Field Radio Surveys. I. Detection Rates and Light Curve Characteristics