XII BLACK HOLES WORKSHOP

Guimarães 19-20^th December 2019

In this work, we study black-hole perturbations in the geometrical representation of the generalized hybrid metric-Palatini gravity. We start by verifying which are the most general conditions on the function (R,\mathcal R)$ that allow for the Kerr solution from GR to be also a solution of this theory. We then perturb the metric tensor, which consequently imposes a perturbation in both the Ricci and Palatini scalar curvatures. To first order in the perturbations, the equations of motion, namely the field equations and the equation that relates the Ricci and the Palatini curvatures can be rewritten in terms of a 4th order wave equation for the perturbation $\delta R$ which can be factorized into two 2nd order massive wave equations for the same variable. The usual ansatz and separation methods are applied and stability bounds on the effective mass of the Ricci perturbation are obtained. These stability regimes are studied case by case and specific forms of the function (R,\mathcal R)$ that allow for stable solutions to exist are obtained

Oral presentation: yes. Poster: no.