We consider extended spiking neural P systems with the additional possibility of so-called “white hole rules”, which send the complete contents of a neuron to other neurons, and we prove that this extension of the original model can easily simulate register machines. Based on this proof, we then define red–green variants of these extended spiking neural P systems with white hole rules and show how to go beyond Turing with these red–green systems. We also discuss the number of actor neurons needed, and the relation of this model to some special variants of Lindenmayer systems.