Boundary-induced corrections to the response of an Unruh-DeWitt detector outside a compact star with Robin surface conditions

Abstract

We formulate the finite-time response problem for a radially accelerated Unruh--DeWitt detector coupled to a real massless scalar field outside a static, spherically symmetric, horizonless compact star. The stellar exterior is described by the Schwarzschild geometry, while unresolved field--surface interactions are represented by a local Robin condition at the stellar radius. After reducing the Klein--Gordon equation to a half-line Schr\"odinger problem, we identify a sufficiently stable branch of the Robin family from positivity of the radial operator, construct delta-normalized continuum modes, and define the static ground state with respect to Schwarzschild time. We derive a mode-amplitude representation of the smoothly switched detector response that avoids a direct numerical treatment of the coincidence singularity of the Wightman distribution. We obtain a radially aligned trajectory of constant signed proper acceleration in terms of the rapidity measured by static observers. The resulting formulation separates the effects of compactness, surface condition, closest approach, detector gap, and interaction duration. We also state the flat-space, Dirichlet, static-detector, low-frequency, large-distance, and long-interaction limits required to validate a numerical implementation. The framework provides a controlled extension of detector studies with static reflective compact objects to finite-time moving probes.