The Evolution of Self-Gravitating Radiating Geodesic Fluid Spheres Instantaneously Admitting a Time-like Killing ^†

In this study, we analyze the effects produced by the sudden appearance of a time-like Killing vector (TKV) on the evolution of radiating geodesic fluids. This is achieved by resorting to the concept of an asymmetry factor, which allows the instantaneous appearance of a given symmetry for a given value of a time-like coordinate. All relevant physical variables are analyzed in detail, showing the imprints of the emergence of TKV at some point in the evolution. The main lesson that can be extracted from the obtained results is that the sudden appearance of a TKV, even for an infinitesimal period of time, drastically changes the subsequent evolution of the system. Of particular relevance is the appearance of a thermal effect linking the asymmetry factor and the relaxation time. The potential applications of these results in the study of gravitational collapse are discussed at the end of the paper.