Recovering the mass and the charge of a Reissner-Nordstr\"om black hole by an inverse scattering experiment

In this paper, we study inverse scattering of massless Dirac fields that propagate in the exterior region of a Reissner-Nordstr\"om black hole. Using a stationary approach we determine precisely the leading terms of the high-energy asymptotic expansion of the scattering matrix that, in turn, permit us to recover uniquely the mass of the black hole and its charge up to a sign

Local energy decay of massive Dirac fields in the 5D Myers-Perry metric

We consider massive Dirac fields evolving in the exterior region of a 5-dimensional Myers-Perry black hole and study their propagation properties. Our main result states that the local energy of such fields decays in a weak sense at late times. We obtain this result in two steps: first, using the separability of the Dirac equation, we prove the absence of a pure point spectrum for the corresponding Dirac operator; second, using a new form of the equation adapted to the local rotations of the black hole, we show by a Mourre theory argument that the spectrum is absolutely continuous. This leads directly to our main result.Comment: 40 page

Near-Field Electromagnetic Tomography Applied to Current Density Reconstruction in Metallized Capacitors

International audienceA nonintrusive method of current cartography inside a component is presented. The measurement of the current density in metallized film capacitors has numerous applications, including nondestructive testing, new component design, and validation of existing models on current distribution in capacitors. The method is based upon the measurement of the magnetic field created by a capacitor and the current density reconstruction by means of inverse problem methodology. The experimental setup comprises of a radio-frequency generator operating between 10 to 1000 MHz, a near-field probe, an XY positioning table and a computer used for control and data acquisition. The first results confirm that, near some frequencies, the current density in the capacitor becomes nonhomogeneous and increases dramatically in some areas

Application of Inverse Problems to current density reconstruction inside components

International audienc