SPEAKER: Anne Franzen (CAMGSD)
ABSTRACT: Motivated by the Strong Cosmic Censorship Conjecture we are interested in stability/instability properties of Cauchy horizons on charged black hole interiors. As a first proxy to the Einstein field equations we consider solutions of the scalar wave equation Box_g phi=0, without symmetry, on fixed black hole backgrounds (cM, g) containing a Cauchy horizon. Previously established decay rates, so called Price's law tails, arising from sufficiently regular data on a two ended Cauchy hypersurface, serve as a starting point for the analysis. The proof depends on energy estimates in the black hole interior which, in combination with commutation by angular momentum operators and application of Sobolev embedding, yield certain stability results at the Cauchy horizon. Finally, we will compare asymptotically flat and asymptotically de Sitter solutions.