A proof of the uniform boundedness of solutions to the wave equation on slowly rotating Kerr backgrounds

Understand

We consider Kerr spacetimes with parameters a and M such that |a|<< M, Kerr-Newman spacetimes with parameters |Q|<< M, |a|<< M, and more generally, stationary axisymmetric black hole exterior spacetimes which are sufficiently close to a Schwarzschild metric with parameter M>0, with appropriate geometric assumptions on the plane spanned by the Killing fields.

• We show uniform boundedness on the exterior for sufficiently regular solutions to the scalar homogeneous wave equation.
• In particular, the bound holds up to and including the event horizon.
• No unphysical restrictions are imposed on the behaviour of the solution near the bifurcation surface of the event horizon.