  Properties of persistent spectral holes (SHs) relevant for frequency
metrology have been investigated in the system $Eu^{3+}:Y_{2}SiO_{5}$ (0.5%) at
crystallographic site 1 and a temperature of $1.2$ Kelvin. Hole linewidths as
small as $0.6~kHz$ have been reliably achieved. The theoretically predicted
$T^4$-dependence of the frequency shift with temperature has been confirmed
with high precision. The thermal hysteresis of the SH frequency between
$1.15~K$ and $4.1~K$ was measured to be less than $6\cdot10^{-3}$ fractionally.
After initially burning a large ensemble of SHs, their properties were studied
on long time scales by probing different subsets at different times. SHs could
still be observed 49 days after burning if not interrogated in the meantime.
During this time, the SH linewidth increased from $4$ to $5.5~kHz$, and the
absorption contrast decreased from 35% to 15%. During a 14-day interval the
absolute optical frequencies of previously unperturbed spectral holes were
measured with respect to a GPS-monitored active H-maser, using a femtosecond
frequency comb. The fractional frequency drift rate exhibited an upper limit of
$2.3\cdot10^{-19} s^{-1}$, 65 times smaller than the most stringent previous
limit.
