  The phase of radio galaxy evolution after the jets have switched off, often
referred to as the remnant phase, is poorly understood and very few sources in
this phase are known. In this work we present an extensive search for remnant
radio galaxies in the Lockman Hole, a well-studied extragalactic field. We
create mock catalogues of low-power radio galaxies based on Monte Carlo
simulations to derive first-order predictions of the fraction of remnants in
radio flux limited samples for comparison with our Lockman-Hole sample. We have
combined LOFAR observations at 150 MHz with public surveys at higher
frequencies to perform a complete selection and have used, for the first time,
a combination of spectral criteria (e.g. the classical ultra-steep spectral
index and high spectral curvature) as well as morphological criteria (e.g. low
radio core prominence and relaxed shapes). Mock catalogues of radio galaxies
are created based on existing spectral and dynamical evolution models combined
with observed source properties. We have identified 23 candidate remnant radio
galaxies which cover a variety of morphologies and spectral characteristics. We
suggest that these different properties are related to different stages of the
remnant evolution. We find that ultra-steep spectrum remnants represent only a
fraction of our remnant sample suggesting a very rapid luminosity evolution of
the radio plasma. Results from mock catalogues demonstrate the importance of
dynamical evolution in the remnant phase of low-power radio galaxies to obtain
fractions of remnant sources consistent with our observations. Moreover, these
results confirm that ultra-steep spectrum remnants represent only a subset of
the entire population ($\sim$50%) when frequencies higher than 1400 MHz are not
included in the selection process, and that they are biased towards old ages.
