Revisiting the theory of scalar cloud: Kerr-Einstein-Maxwell-Dilaton-Axion black hole

In this work, we present the novel exact scalar cloud solution in the Einstein-Maxwell-Dilaton-Axion (EMDA) theory. Traditionally, the scalar cloud is examined using an approximation approach known as the AAM technique, which operates in the ultralight scalar field and low black hole spin regimes. The objective of this work is to revisit the theory of the scalar cloud of the black hole by first deriving the exact solution of the massive Klein-Gordon equation in the Kerr-EMDA black hole spacetime. We discover that the scalar cloud exact solution is achieved using the Confluent Heun function and its exact spectrum conforms to the polynomial condition of the radial solution. Working with the novel exact solution allows us to investigate the scalar cloud without being constrained by ultralight scalar mass or the slow black hole limit. Finally, we discover that the precise characteristic frequency of the black hole’s scalar cloud accounts for the influence of both the event horizon and the Cauchy horizon.