The ďAlembert solution in hyperboloidal foliations

Abstract: We explicitly construct the analogue of the \v{d}Alembert solution to the 1+1 wave equation in an hyperboloidal setting. This hyperboloidal \v{d}Alembert solution is used, in turn, to gain intuition into the behaviour of solutions to the wave equation in a hyperboloidal foliation and to explain some apparently anomalous behaviour observed in numerically constructed solutions discussed in the literature.