Boundedness and decay for the Teukolsky system of spin $\pm2$ on Reissner-Nordstr\"om spacetime: the case $|Q| \ll M$

Understand

We prove boundedness and polynomial decay statements for solutions to the spin $\pm2$ generalized Teukolsky system on a Reissner-Nordstr\"om background with small charge.

• The first equation of the system is the generalization of the standard Teukolsky equation in Schwarzschild for the extreme component of the curvature $\alpha$.
• The second equation, coupled with the first one, is a new equation for a new gauge-invariant quantity involving the electromagnetic curvature components.
• The proof is based on the use of derived quantities, introduced in previous works on linear stability of Schwarzschild.