Gravito-electromagnetic perturbations of MOG black holes with a cosmological constant: Quasinormal modes and Ringdown waveforms

Abstract

In this paper, we present black hole solutions with a cosmological constant in the MOG theory, where the strength of the gravitational constant is determined by $G = G_\text{N}(1+\alpha)$. We derive the master equations for gravito-electromagnetic perturbations and numerically solve for the Quasinormal Mode (QNM) spectrum and the ringdown waveforms. Our results show that increasing either the MOG parameter $\alpha$ or the cosmological constant $\Lambda$ leads to a decrease in both the real and imaginary parts of the QNM frequencies for electromagnetic and gravitational modes, compared to standard Schwarzschild-de Sitter (S-dS) or MOG black holes, respectively. Meanwhile, the result indicates that in the MOG-de Sitter spacetime, the frequencies for electromagnetic and gravitational modes display strict isospectrality, and exhibit the same ringdown waveforms. Our findings have implications for the ringdown phase of mergers involving massive compact objects, which is of particular relevance given the recent detections of gravitational waves by LIGO.Comment: 16pages, 6 figure