Shadows and quasinormal modes of rotating black holes in Horndeski theory: Parameter constraints using EHT observations of M87* and Sgr A*

One way to test the presence of scalar & vector fields in the spacetime of black holes is to get constraints on the fields and black hole parameters using astrophysical observations such as black hole shadow, quasiperiodic oscillations, etc. In this work, we aimed to investigate spacetime properties around black holes in Horndeski gravity. First, we obtain a rotating black hole solution using the Newman–Janis Algorithm (NJA), and we study the event horizon, statistic limits, and ergoregion of the black hole spacetime. In addition, we calculate the effective gravitational mass of the black hole. We derive equations for null geodesics and show the combined effects of the black hole spin and Horndeski gravity parameter on the shadow shape of the black hole and its radius distortion. We find that black hole spin and Horndeski parameters cause an increase in the values of shadow radius and its deformation. Next, we obtain constraints for the upper and lower values for black hole spin and Horndeski parameters using event horizon telescope (EHT) data from Sgr A* and M87*shadow sizes. Finally, we investigated the shadow radius, equatorial, and polar quasinormal modes using the geometric-optic relationship between the parameters of the quasinormal mode and the conserved values along the geodesics in the spacetime of the rotating Horndeski black hole.