Gravity seminar - Anne Franzen Seminar

 

Motivated by the Strong Cosmic Censorship Conjecture we consider solutions of the scalar wave equation \Box_g\phi=0, without symmetry, on fixed subextremal Reissner-Nordstrom backgrounds (\cM,g) with nonvanishing charge. Previously, it has been shown that for \phi arising from sufficiently regular data on a two ended Cauchy hypersurface, the solution and its derivatives decay suitably fast on the event horizon \cH^+. Using this, we show here that \phi is in fact uniformly bounded, |\phi| <= C, in the black hole interior up to and including the bifurcate Cauchy horizon \cC\cH^+, to which \phi in fact extends continuously. We will discuss how the Strong Cosmic Censorship Conjecture should be defined for this set up and what the model might indicate for the full non-linear case. If time permits we will also discuss how the analysis has to be extended in order to investigate solutions to the scalar waves equation on fixed Kerr backgrounds.