Scalar field conformally coupled to a charged BTZBTZ black hole

We study the Klein–Gordon equation of a scalar field conformally coupled to a charged BTZBTZ black hole. The background metric is obtained by coupling a non-linear and conformal invariant Maxwell field to (2+1)(2+1) gravity. We show that the radial part is generally solved by a Heun function and, in the pure gravity limit, by a hypergeometric function.