Quasinormal modes in the field of a dyon-like dilatonic black hole

Quasinormal modes of massless test scalar field in the background of gravitational field for a non-extremal dilatonic dyonic black hole are explored. The dyon-like black hole solution is considered in the gravitational 4 d model involving two scalar fields and two 2-forms. It is governed by two 2-dimensional dilatonic coupling vectors λ ᵢ λ i obeying λ ᵢ (λ ₁ + λ ₂) > 0 λ i ( λ 1 + λ 2 ) > 0 , $$i =1,2$$ i = 1 , 2 . The first law of black hole thermodynamics is given and the Smarr relation is verified. Quasinormal modes for a massless scalar (test) field in the eikonal approximation are obtained and analysed. These modes depend upon a dimensionless parameter a ( 0 < a ≤ 2 0 < a ≤ 2 ) which is a function of λ ᵢ λ i . For limiting strong ( $$a = +0$$ a = + 0 ) and weak ( $$a = 2$$ a = 2 ) coupling cases, they coincide with the well-known results for the Schwarzschild and Reissner–Nordström solutions. It is shown that the Hod conjecture, connecting the damping rate and the Hawking temperature, is satisfied for 0 < a ≤ 1 0 < a ≤ 1 and all allowed values of parameters.