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We study the solutions of the wave equation where a massless scalar field iscoupled to the Wahlquist metric, a type-D solution. We first take the fullmetric and then write simplifications of the metric by taking some of theconstants in the metric null. When we do not equate any of the arbitraryconstants in the metric to zero, we find the solution is given in terms of thegeneral Heun function, apart from some simple functions multiplying thissolution. This is also true, if we equate one of the constants $Q_0$ or $a_1$to zero. When both the NUT-related constant $a_1$ and $Q_0$ are zero, thesingly confluent Heun function is the solution. When we also equate theconstant $\nu_0$ to zero, we get the double confluent Heun-type solution. Inthe latter two cases, we have an exponential and two monomials raised to powersmultiplying the Heun type function. Thus, we generalize the Batic et al. resultfor type-D metrics for this metric and show that all variations of theWahlquist metric give Heun type solutions.

A massless scalar particle coupled to the Wahlquist metric