We consider the problem of communication over a continuous-time Poisson channel subject to a covertness constraint: The relative entropy between the output distributions when a message is transmitted and when no input is provided must be small. In the absence of both bandwidth and peak-power constraints, we show the covert communication capacity of this channel, in nats per second, to be infinity. When a peak-power constraint is imposed on the input, the covert communication capacity becomes zero, and the “square-root scaling law” applies. When a bandwidth constraint but no peak-power constraint is imposed, the covert communication capacity is again shown to be zero, but we have not determined whether the square-root law holds or not.
