Stability of Kerr black holes in generalized hybrid metricPalatini gravity
Abstract
It is shown that the Kerr solution exists in the generalized hybrid metricPalatini gravity theory and that for certain choices of the function f (R ,R ) that characterizes the theory, the Kerr solution can be stable against perturbations on the scalar degree of freedom of the theory. We start by verifying which are the most general conditions on the function f (R ,R ) that allow for the general relativistic Kerr solution to also be a solution of this theory. We perform a scalar perturbation in the trace of the metric tensor, which in turn imposes a perturbation in both the Ricci and Palatini scalar curvatures. To first order in the perturbation, the equations of motion, namely the field equations and the equation that relates the Ricci and the Palatini curvature scalars, can be rewritten in terms of a fourthorder wave equation for the perturbation δ R which can be factorized into two secondorder 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 scalar perturbation are obtained. These stability regimes are studied case by case and specific forms of the function f (R ,R ) that allow for a stable Kerr solution to exist within the perturbation regime studied are obtained.
 Publication:

Physical Review D
 Pub Date:
 February 2020
 DOI:
 10.1103/PhysRevD.101.044055
 Bibcode:
 2020PhRvD.101d4055R