Quasinormal Modes in First-Order Modified Gravitation
Quasinormal Modes; Modified Gravity; Black Holes; Scalar Perturbations; Einstein Frame.
The detection of gravitational waves has ushered in a new era in black hole physics, enabling tests of General Relativity (GR) in strong-field regimes through the analysis of the ringdown phase and Quasinormal Modes (QNMs). This dissertation investigates the perturbative behavior of Schwarzschild black holes within the context of a Modified Gravity theory that includes higher-order corrections in the action, specifically in first order terms (R^2 e R\Box R). By employing a conformal transformation to map the system from the Geometric Frame to the Einstein Frame, we demonstrate that the higher-order field equations can be recast as a second-order system coupled to massive auxiliary scalar fields. The linearized analysis reveals that the tensor sector of metric perturbations remains isospectral to GR forodd-parity (axial) modes, due to the diagonal structure of the background. However, "new physics" manifests in the scalar sector, whose quasinormal frequencies were calculated numerically using Leaver's Continued Fraction and Hill's Determinant methods. The results indicate that the presence of the scalar field's effective mass alters the frequency spectrum, reducing the damping rate and allowing for the existence of long-lived modes for masses above a critical threshold. It is concluded that, in this class of theories, the signature of modified gravity lies primarily in the excitation of extra scalar degrees of freedom, while the stability of the Schwarzschild vacuum solution is preserved.