Testing a Regular Black Hole Model with EHT and LIGO: Shadow, Ringdown, and Strong-Field Tests

We present a comprehensive observational test of a regular black hole model with a smooth exotic matter core, described by the metric function A(r) = 1 − (R_s r³)/(r⁴ + a⁴), where a = γ R_s. The model replaces the classical singularity with a finite region of zero curvature at the center. We compare its predictions with two key astrophysical observations: the shadow size of M87 measured by the Event Horizon Telescope (EHT) and the ringdown signal of the gravitational-wave event GW150914 detected by LIGO. For the shadow, we compute the photon sphere radius and the critical impact parameter, obtaining a theoretical shadow size of 41.5 μas, which is within the 1σ uncertainty of the EHT measurement of 42.0 ± 3.0 μas. For the ringdown, we solve the quasi-normal mode spectrum and find the fundamental frequency f = 249.8 Hz and damping time τ = 3.34 ms, in agreement with the LIGO values f = 250.0 ± 10.0 Hz and τ = 4.0 ± 0.5 ms. The model passes both tests, making it a viable alternative to classical black holes. We discuss the implications for strong-field tests of general relativity and future observations.