Quasinormal modes and the correspondence with shadow in black holes with a deficit solid angle and quintessence-like matter

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In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a $4$-dimensional black hole with a deficit solid angle and quintessence-like matter.

• We find that the radii of the photon sphere and shadow decrease with the decreases of the deficit solid angle and density of quintessence-like matter.
• The quasinormal modes are gotten by the sixth order WKB approximation method and shadow radius, respectively.
• The values of the real part and imaginary parts of the quasinormal modes increase with the decrease of the values of the deficit solid angle and density of quintessence-like matter when the multipole number is fixed.