  Stars within the innermost part of the Nuclear Star Cluster can reach orbital
velocities up to a few percent of the light speed. As analyzed by Rafikov
(2020), Doppler boosting of stellar light may be of relevance at the pericenter
of stellar orbits, especially with the upcoming high-precision photometry in
the near- and mid-infrared bands. Here we analyze the previously neglected
effect of infrared spectral index of monitored objects on the Doppler-boosted
continuum emission in a narrow band. In contrast to main-sequences stars, the
detected compact infrared-excess dust-enshrouded objects have an enhanced
Doppler-boosting effect by as much as an order of magnitude, with the
variability amplitude of the order of ten percent for the most eccentric
orbits. In a similar way, pulsars dominated by non-thermal synchrotron emission
are also expected to exhibit a stronger Doppler-boosted signal by a factor of
at least four in comparison with canonical S stars. In case the stellar orbit
is robustly determined, the relative flux variation can thus provide hints
about the nature of the objects. For extended dust-enshrouded objects, such as
G1, that are variable due to tidal, ellipsoidal, bow-shock, and irradiation
effects, the subtraction of the expected Doppler-boosting variations will help
to better comprehend their internal physics. In addition, the relative flux
variability due to higher-order relativistic effects is also modified for
different negative spectral indices in a way that it can obtain both positive
and negative values with the relative variability of the order of one percent.
