  The double copy is a remarkable relationship between gauge theory and gravity
that has been explored in a number of contexts, most notably scattering
amplitudes and classical solutions. The convolutional double copy provides a
straightforward method to bridge the two theories via a precise map for the
fields and symmetries at the linearised level. This method has been thoroughly
investigated in flat space, offering a comprehensive dictionary both with and
without fixing the gauge degrees of freedom. In this paper, we extend this to
curved space with an (anti) de Sitter background metric. We work in the
temporal gauge, and employ a modified convolution that involves the Mellin
transformation in the time direction. As an example, we show that the
point-like charge in gauge theory double copies to the (dS-) Schwarzschild
black hole solution.
