  We study the instabilities of a particle-hole symmetric Weyl metal with both
electron and hole Fermi surfaces (FS) around the Weyl points. For a repulsive
interaction, we find that the leading instability is towards a longitudinal
spin-density-wave order (SDW$_z$). Besides, there exist three degenerate
subleading instabilities: a charge-density-wave (CDW) instability and two
transverse spin-density-wave (SDW$_{x,y}$) instabilities. For an attractive
interaction the leading instabilities are towards two pair-density-wave orders
(PDW) which pair the two FS's separately. Both the PDW and SDW$_z$ order
parameters fully gap out FS's, while the CDW and SDW$_{x,y}$ ones leave line
nodes on both FS's. For the SDW$_z$ and the PDW states, the surface Fermi arc
in the metallic state evolves to a chiral Fermi line which passes the
projection of the Weyl points and traverses the full momentum space. For the
CDW state, the line node projects to a "drumhead" band localized on the
surface, which can lead to a topological charge polarization. We verify the
surface states by numerically simulating the angular-resolved photoemission
spectroscopy data.
