A seal assembly for a gas turbine includes a seal case, and a seal shoe arranged within the seal case. The seal shoe includes a main seal portion that is configured to engage with a radial bearing engagement portion of a rotor shaft, a radial bearing surface that engages with the radial bearing engagement portion of the rotor shaft, at least one hydrodynamic lift cavity extending through the radial bearing surface, and at least one airflow passage extending from a first side of the seal shoe through the at least one hydrodynamic lift cavity and providing airflow communication between the first side of the seal shoe and the at least one hydrodynamic lift cavity.