  The theoretical understanding of the spin-orbit coupling (SOC) effects at
LaAlO$_{3}$/SrTiO$_{3}$ interfaces and SrTiO$_{3}$ surfaces is still in its
infancy. We perform first-principles density-functional-theory calculations and
derive from these a simple tight-binding Hamiltonian, through a Wannier
function projection and group theoretical analysis. We find striking
differences to the standard Rashba theory for spin-orbit coupling in
semiconductor heterostructures due to multi-orbital effects: by far the biggest
SOC effect is at the crossing point of the $xy$ and $yz$ (or $zx$) orbitals;
and around the $\Gamma$ point a Rashba spin splitting with a cubic dependence
on the wave vector $\vec{k}$ is possible.
