  Finite-momentum pairing in a Pauli-limited spin-singlet superconductor arises
from the pair-breaking effects of an external Zeeman field, a mechanism which
is not applicable in odd-parity spin-triplet superconductors. However, in
multiorbital systems, the relevant bands originating from different orbitals
are usually separated in momentum space, implying that orbital-singlet pairing
is a natural candidate for a finite-momentum pairing state. We show that
finite-momentum pairing arises in even-parity orbital-singlet spin-triplet
superconductors via the combination of orbitally-nontrivial kinetic terms and
Hund's coupling. The finite-momentum pairing is then suppressed with an
increasing spin-orbit coupling, stabilizing a uniform pseudospin-singlet
pairing. We also examine the effects of the magnetic field and find
field-induced superconductivity at large fields. We apply these findings to the
multiorbital superconductor with spin-orbit coupling, Sr$_{2}$RuO$_{4}$ and
show that a finite-momentum pseudospin-singlet state appears between the
uniform pairing and normal states. Future directions of inquiry relating to our
findings are also discussed.
