The occurrence of planets and other substellar bodies around white dwarfs using K2

The majority of stars both host planetary systems and evolve into a white dwarf (WD). To understand their post-main-sequence (PMS) planetary system evolution, we present a search for transiting/eclipsing planets and other Substellar Bodies (SBs) around WDs using a sample of 1148 WDs observed by K2. Using transit injections, we estimate the completeness of our search. We place constraints on the occurrence of planets and substellar bodies around white dwarfs as a function of planet radius and orbital period. For short-period ($P < 40$days)smallobjects,fromasteroid-sizedto$1.5 \ R_{\oplus}$, these are the strongest constraints known to date. We further constrain the occurrence of hot Jupiters ($<1.5\mathrm{\%}$), habitable zone Earth-sized planets ($<28\mathrm{\%}$), and disintegrating short-period planets ($\sim 12\mathrm{\%}$). We blindly recovered all previously known eclipsing objects, providing confidence in our analysis, and make all light curves publicly available.