  The plethora of photometric data collected by the Kepler space telescope has
promoted the detection of tens of thousands of stellar rotation periods.
However, these periods are not found to an equal extent among different
spectral types. Interestingly, early G-type stars with near-solar rotation
periods are strongly underrepresented among those stars with known rotation
periods. In this study we investigate whether the small number of such stars
can be explained by difficulties in the period determination from photometric
time series. For that purpose, we generate model light curves of early G-type
stars with solar rotation periods for different inclination angles,
metallicities and (magnitude-dependent) noise levels. We find that the
detectability is determined by the predominant type of activity (i.e. spot or
faculae domination) on the surface, which defines the degree of irregularity of
the light curve, and further depends on the level of photometric noise. These
two effects significantly complicate the period detection and explain the lack
of solar-like stars with known near-solar rotation periods. We conclude that
the rotation periods of the majority of solar-like stars with near-solar
rotation periods remain undetected to date. Finally, we promote the use of new
techniques to recover more periods of near-solar rotators.
