Exact investigation into plasma augmented gravitational atom

Abstract We present an analytical study of quasibound scalar configurations in a four-dimensional Einstein–Skyrme black hole immersed in a cold, non-magnetized plasma. By solving the Klein–Gordon equation in closed form, we obtain the corresponding wave functions and a complex quasibound spectrum, where the real part determines the binding energy while the imaginary part characterizes the decay rate of the modes. The plasma environment is modeled through power-law density profiles of the form constant ( $$h=0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ), inverse ( $$h=1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> ), and inverse-square ( $$h=2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>h</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> ). We show that for the constant profile the plasma contributes to the damping of the quasibound states without modifying the leading-order binding energy. For the inverse profile, the plasma introduces a nontrivial interplay with the Skyrme sector, which can lead to a significant reduction of the decay rate under a specific parameter balance, while the modes remain generically stable. In contrast, for the inverse-square profile the plasma contribution vanishes at the considered order, and the spectrum reduces to that of the vacuum Einstein–Skyrme configuration. In all cases, the imaginary part of the frequency remains negative within the parameter range studied and no exponentially growing modes are found. Consequently, neither superradiant amplification nor black-hole bomb instabilities arise in this setup. These results establish the Einstein–Skyrme spacetime as an exactly solvable framework for studying scalar wave propagation in nonlinear gravitational and dispersive media.