  Finding solar siblings, that is, stars that formed in the same cluster as the
Sun, will yield information about the conditions at the Sun's birthplace. We
search for solar sibling candidates in AMBRE, the very large spectra database
of solar vicinity stars. Since the ages and chemical abundances of solar
siblings are very similar to those of the Sun, we carried out a chemistry- and
age-based search for solar sibling candidates. We used high-resolution spectra
to derive precise stellar parameters and chemical abundances of the stars. We
used these spectroscopic parameters together with Gaia DR2 astrometric data to
derive stellar isochronal ages. Gaia data were also used to study the
kinematics of the sibling candidates. From the about 17000 stars that are
characterized within the AMBRE project, we first selected 55 stars whose
metallicities are closest to the solar value (-0.1 < [Fe/H] < 0.1 dex). For
these stars we derived precise chemical abundances of several iron-peak, alpha-
and neutron-capture elements, based on which we selected 12 solar sibling
candidates with average abundances and metallicities between -0.03 to 0.03 dex.
Our further selection left us with 4 candidates with stellar ages that are
compatible with the solar age within observational uncertainties. For the 2 of
the hottest candidates, we derived the carbon isotopic ratios, which are
compatible with the solar value. HD186302 is the most precisely characterized
and probably the most probable candidate of our 4 best candidates. Very precise
chemical characterization and age estimation is necessary to identify solar
siblings. We propose that in addition to typical chemical tagging, the study of
isotopic ratios can give further important information about the relation of
sibling candidates with the Sun. Ideally, asteroseismic age determinations of
the candidates could solve the problem of imprecise isochronal ages.
