Abstract
Time-domain astrophysics provides a unique opportunity to study the most extreme physical processes in the Universe, including the deaths of massive stars, the creation and mergers of compact objects like neutron stars and black holes, and the tidal disruption of stars by supermassive black holes. I will discuss my recent and ongoing work to reveal the formation and structure of relativistic jets and outflows in the most extreme astrophysical transients, including gamma-ray bursts (GRBs) and tidal disruption events (TDEs). I will further show that radio data provide the best constraints on the immediate environments of these transients, probing models of black hole growth and accretion (TDEs) and stellar evolution (GRBs). Finally, I will discuss the bright future of time-domain astrophysics. With the pioneering detections of gravitational waves, astronomers and physicists have gained a new, complementary tool to study compact object mergers, with implications for fields as wide-ranging as general relativity, nuclear physics, cosmology, and shock physics. Collaboration with LIGO and its successor gravitational wave observatories will enable precision constraints on merger physics, while upcoming surveys like LSST 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.