Numerical and observational evidence suggests that massive white dwarfs dominate the innermost regions of core-collapsed globular clusters by both number and total mass. Using NGC 6397 as a test case, we constrain the features of white dwarf populations in core-collapsed clusters, both at present day and throughout their lifetimes. The dynamics of these white dwarf subsystems have a number of astrophysical implications. We demonstrate that the collapse of globular cluster cores is ultimately halted by the dynamical burning of white dwarf binaries. We predict core-collapsed clusters in the local universe yield a white dwarf merger rate of $mathcal{O}(10rm{),Gpc}^{-3},rm{yr}^{-1}$, roughly $0.1-1%$ of the observed Type Ia supernova rate. We show that prior to merger, inspiraling white dwarf binaries will be observable as gravitational wave sources at milli- and decihertz frequencies. Over $90%$ of these mergers have a total mass greater than the Chandrasekhar limit. If the merger/collision remnants are not destroyed completely in an explosive transient, we argue the remnants may be observed in core-collapsed clusters as either young neutron stars/pulsars/magnetars (in the event of accretion-induced collapse) or as young massive white dwarfs offset from the standard white dwarf cooling sequence. Finally, we show collisions between white dwarfs and main sequence stars, which may be detectable as bright transients, occur at a rate of $mathcal{O}(100rm{),Gpc}^{-3},rm{yr}^{-1}$ in the local universe. We find that these collisions lead to depletion of blue straggler stars and main sequence star binaries in the centers of core-collapsed clusters.
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