Observing the eye of the storm I: testing regular black holes with LVK and EHT observations

According to the celebrated singularity theorems, space-time singularities in general relativity are inevitable. However, it is generally believed that singularities do not exist in nature, and their existence suggests the necessity of a new theory of gravity. In this paper, we investigated a regular astrophysically viable space-time (regular in the sense that it is singularity-free) from the observational point of view using observations from the LIGO, Virgo, and KAGRA (LVK), and the event horizon telescope (EHT) collaborations. This black hole solution depends on a free parameter $\ell$ in addition to the mass, $M$, and the spin, $a$, violating, in this way, the non-hair theorem/conjecture. In the case of gravitational wave observations, we use the catalogs GWTC-1, 2, and 3 to constrain the free parameter. In the case of the EHT, we use the values of the angular diameter reported for SgrA* and M87*. We also investigated the photon ring structure by considering scenarios such as static spherical accretion, infalling spherical accretion, and thin accretion disk. Our results show that the EHT observations constrain the free parameter $\ell$ to the intervals $0\leq \ell \leq 0.148$ and $0\leq \ell \leq 0.212$ obtained for SgrA* and M87*, respectively. On the other hand, GW observations constrain the free parameter with values that satisfy the theoretical limit, particularly those events for which $\ell<<1$. Our results show that the most stringent constraints on $\ell$ correspond to the events GW191204-171526 ($\ell=0.041^{+0.106}_{-0.041}$) and GW190924-021846 ($\ell=0.050^{+0.165}_{-0.050}$) for the SEOB model.