The First Multi-Messenger Nova: External Shocks, TeV Photons, and Neutrinos in the Next Eruption of T CrB
T Coronae Borealis is the most compelling anticipated Galactic recurrent nova and one of the best opportunities to test whether nova eruptions can become genuine multi-messenger transients. Recent observational work on classical novae has shown that the GeV $\gamma$-ray luminosity correlates strongly with the differential velocity between interacting outflows, suggesting that shock power depends strongly on velocity contrast. We apply this empirical framework to T CrB and compare it with the 2021 eruption of RS Ophiuchi, the only nova securely detected at TeV energies. We argue that T CrB may lie at the extreme high-$\Delta v$ end of the nova population and that its strongest shock should arise at the external interaction between the nova ejecta and the slow circumbinary medium. This makes the external shock the most likely site of any TeV emission, while the GeV signal may contain contributions from both internal, if present, and external shocks. Because T CrB is substantially closer than RS Oph, it is an especially favorable target for TeV detection. The neutrino case is promising but more uncertain because it depends sensitively on the density and structure of the circumbinary material. We also revisit the recurrence time of T CrB. Using the observed scatter of better-sampled recurrent novae, we infer a representative population-scale recurrence of $T_{\rm rec}\simeq80\pm12$ yr. Taken together, its proximity and potentially extreme shock velocities make T CrB perhaps the best opportunity for a nova to become the first securely established multi-messenger nova.