Observational astronomy shows an abundance of transient sources, from supernovae to gamma-ray bursts and active galactic nuclei (AGN) including quasars and blazars. Future observations may reveal mirror images in gravitational waves with LIGO (US), Virgo (France-Italy) and the planned LISA spacebased mission. Based on a review of current observations, transients may be teaching us just the kind of physics that is far beyond what we study in the laboratory (including the LHC), such as the creation of ultra-high energy cosmic rays (recently associated with AGN by the Pierre Auger collaboration), bursts of gravitational waves from black hole mergers, the creation of Bekenstein-Hawking entropy in black hole spin-down, and the formation of ultra-relativistic jets. Astrophysical transients thus define some first-principle problems in mathematical physics, such as modeling the interaction of matter with spinning black holes and efficient numerical methods for the evolution of black hole spacetimes in the complex plane. The results are of practical use to searches for gravitational radiation by LIGO-Virgo and LISA.