Transient Astrophysics Probe: White Paper. [Decadal Survey on Astronomy and Astrophysics (Astro2020)]

The Transient Astrophysics Probe (TAP) is a wide-field multi-wavelength transient mission proposed for flight starting in the late 2020s. The mission instruments include unique ``Lobster-eye'' imaging soft X-ray optics that allow an approximately 1600-degrees-squared Field of View (FoV); a high sensitivity, 1-degree-squared FoV soft X-ray telescope; a 1-degree-squared FoV Infrared telescope with bandpass 0.6 to 3 microns; and a set of 8 NaI gamma-ray detectors. TAP's most exciting capability will be the observation of tens per year of X-ray and Infrared counterparts of gravitational waves (GWs) involving stellar-mass black holes and neutron stars detected by LIGO (Laser Interferometer Gravitational-Wave Observatory ) / Virgo / KAGRA (Kamioka (Japan) Gravitational Wave Detector) / LIGO-India, and possibly several per year X-ray counterparts of GWs from supermassive black holes, detected by LISA (Laser Interferometer Space Antenna) and Pulsar Timing Arrays. TAP will also discover hundreds of X-ray transients related to compact objects, including tidal disruption events, supernova shock breakouts, and Gamma-Ray Bursts from the epoch of reionization.