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Analogue Black String Realized in a Damped Quantum Harmonic Oscillator

A massive scalar field in a chargeless static black-string spacetime obeys a Klein-Gordon equation whose radial part is a biconfluent Heun equation with purely imaginary energy eigenvalues (quasinormal-mode signatures). The same biconfluent Heun equation governs a damped quantum harmonic oscillator built from coupled mass-spring elements, giving a table-top analogue that emulates the black-string scalar field.