Gravitational perturbations of a regular T-dulatiy inspired black hole: Quasinormal modes, excitation factors, and time-domain evolution

We study axial gravitational perturbations of the neutral regular black hole generated by a non-local, T-duality-inspired zero-point length and the associated gravitational self-energy. In this geometry, the usual point source is replaced by a regular core, and the zero-point length controls the departure from the Schwarzschild limit. We compute the fundamental quasinormal modes and several overtones using high-order WKB--Padé methods, and we verify the dominant mode via direct time-domain evolution. When the zero-point length is turned on, the real parts of the ADM-scaled frequencies increase for the gravitational modes with $\ell=2,3,4$, so the ringdown oscillates faster than in the Schwarzschild limit. The damping rates change more gradually: they initially increase slightly and then decrease near the largest deformation values considered here. This behavior is consistent with the effective potential, whose barrier becomes higher as the deformation parameter increases. We also compute the corresponding excitation factors and find that their magnitudes vary much less strongly than the quasinormal frequencies.

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