Time-domain astrophysics provides a unique opportunity to study the most extreme physical processes in the Universe, including the deaths of massive stars, the destruction and creation of compact objects like neutron stars and black holes, and the tidal disruption of stars by supermassive black holes (SMBHs). With the pioneering detections of gravitational waves, astronomers and physicists have gained a new, complementary tool to study these cataclysmic events, with implications for fields as wide-ranging as general relativity, nuclear physics, cosmology, and shock physics. The full richness of these synergies has barely begun to be realized, and will take decades to exploit fully.
My research program uses radio observations in combination with multi-wavelength data and gravitational wave detections to study the most extreme classes of astrophysical transients, including gamma-ray bursts (GRBs) and tidal disruption events (TDEs). I will discuss my recent results that reveal the formation and structure of relativistic jets and outflows in these systems. I will also show that radio data provide the best constraints on the density of the surrounding medium, probing models of SMBH growth and accretion (TDEs) and stellar evolution models (GRBs). Finally, I will discuss the bright future of time-domain astrophysics. Upcoming decades will see a revolution in this field: collaboration with LIGO and its successor GW observatories will enable precision constraints on merger physics, while large surveys like LSST and SDSS-V will provide the first large samples of rare, relativistic events and move transient science into the statistical realm. Simultaneously, new radio interferometers like the ngVLA and the Square Kilometer Array are poised to transform radio astronomy, revealing the radio sky in unprecedented depth and leading to the discovery of relativistic transient populations in the radio band.