Tachyonic modes as a resonant system in weakly curved stellar spacetimes

Abstract

A real scalar field nonminimally coupled to the curvature of an astrophysical object can develop an effective potential that supports, alongside stable oscillatory solutions, a set of tachyonic modes with purely imaginary frequencies. Focusing on constant-density Newtonian stars, we show that the tachyonic sector behaves as a collection of decoupled inverted harmonic oscillators, whose quantization is naturally addressed within the rigged Hilbert space formalism. At the quantum level, this sector is described by resonant states, with mean lifetimes determined by the associated imaginary frequencies. To probe the physical implications of this framework, we compute the transition probability of an Unruh-DeWitt detector in a circular orbit. In the presence of tachyonic modes, the detector response acquires an additional finite Lorentzian profile that modifies the standard circular Unruh-like background.