In the Bardeen and Hayward black hole families, the singular type II branch can have two light rings and echo-like quasinormal signals, while regular black holes have one light ring.
Universal relations for quasinormal modes of neutron stars in $R^2$ gravity
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abstract
We construct quasinormal modes for neutron stars in $R^2$ gravity in the Einstein frame, considering scalar masses in the sub-neV range. In particular, we investigate the fundamental quadrupole fluid f-modes and the dipole fluid F-modes. Employing six equations of state covering matter content with nucleons, hyperons, and quarks, we then propose universal relations for the quadrupole f-modes and dipole F-modes. The dipole F-modes are ultra-long lived and, for the lower scalar masses, their frequencies are inversely proportional to the corresponding Compton wavelength.
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Can we distinguish whether black holes have singularities or not through echoes and light rings?
In the Bardeen and Hayward black hole families, the singular type II branch can have two light rings and echo-like quasinormal signals, while regular black holes have one light ring.