Self-Trapping of G-Mode Oscillations in Relativistic Thin Disks, Revisited II: Revision of Boundary Condition

In a previous paper (Kato 2017a) we have examined how the self-trapping of g-mode oscillations in geometrically thin relativistic disks is affected by the presence of uniform vertical magnetic fields. Disks considered are isothermal in the vertical direction and are truncated at a certain height by presence of hot corona. After a correction of simple analytical error, we showed (Kato 2017b) that the self-trapping of axisymmetric g-mode oscillations in non-magnetized disks is destroyed by weak magnetic fields as Fu and Lai (2009) showed. In this paper, however, we re-examine the same problem by imposing a different more relevant boundary condition on the disk-corona surface and find that the self-trapping of axisymmetric g-mode oscillations seems to still exist like the case of non-magnetized disks.