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Mokdad Mokdad

Publications and source records attributed to Mokdad Mokdad.

7 recordsLinked to original sources
arXiv2023

Scattering of Dirac Fields in the Interior of Kerr-Newman(-Anti)-de Sitter Black Holes via Comparison and Symmetry Operators

In this paper we construct a scattering theory for the massive and charged Dirac fields in the interiors of sub-extremal Kerr-Newman(-anti)-de Sitter black holes. More precisely, we show existence, uniqueness and asymptotic completeness of scattering data for such Dirac fields from the event horizon of the black hole to the Cauchy horizon. Our approach relies on constructing the wave operators where the Hamiltonian of the full dynamics is time-dependent. To prove asymptotic completeness, we use two methods. The first involves a comparison operator, while for the second we introduce and employ a symmetry operator of the Dirac equation.

gr-qc↗
arXiv2022

On the Scattering of Waves inside Charged Spherically Symmetric Black Holes

In this paper we show that there is a breakdown of scattering between the event horizon (or the Cauchy horizon) and an intermediate Cauchy hypersurface in the dynamic interior of a Reissner-Nordström-like black hole. More precisely, we show that the trace operators and their analytic counterparts, the inverse wave operators, do not have bounded inverses, even though these operators themselves are bounded. This result holds for the natural energy given by the energy-momentum tensor of the wave equation using the timelike vector field of the Regge-Wheeler variable, which asymptotically becomes normal to the horizons. The behaviour of solutions at low spatial-frequencies and their behaviour at high angular momenta are the only obstructions causing this breakdown of scattering. The breakdown follows from an analysis of a $1+1$-dimensional wave equation with exponentially decaying potential which we treat for general potentials, and we show that the breakdown is generic.

gr-qc↗
arXiv2021

Conformal Scattering and the Goursat Problem for Dirac Fields in the Interior of Charged Spherically Symmetric Black Holes

We construct a conformal scattering theory for Dirac fields in the interior of a Reissner-Nordström-like black hole, between the black hole event horizon and the Cauchy horizon. The main result is a resolution of the characteristic Cauchy problem for the Dirac equation on the horizons by solving a system of wave equations and re-interpreting its solution as the components of the required Dirac solution.

gr-qc↗
arXiv2017

Conformal Scattering of Maxwell Fields on Reissner-Nordstrøm-de Sitter Black Hole Spacetimes

We construct a complete conformal scattering theory for Maxwell fields in the static exterior region of a Reissner-Nordstrøm-de Sitter black bole spacetime. This is done using uniform energy decay results that we obtain in a separate paper, to show that the trace operators are injective and have closed ranges. We then solve the Goursat problem (characteristic Cauchy problem) for Maxwell fields on the null boundaries showing that the trace operators are also surjective.

gr-qc↗
arXiv2017

Decay of Maxwell Fields on Reissner-Nordstrøm-de Sitter Black Holes

In this paper we use Morawetz estimates with geometric energy estimates -the so-called vector field method- to prove decay results for the Maxwell field in the static exterior region of the Reissner-Nordstrøm-de Sitter black hole. We prove two types of decay: The first is a uniform decay of the energy of the Maxwell field on achronal hypersurfaces as the hypersurfaces approach timelike infinities. The second decay result is a pointwise decay in time with a rate of $t^{-1}$ which follows from local energy decay by Sobolev estimates. Both results are consequences of bounds on the conformal energy defined by the Morawetz conformal vector field. These bounds are obtained through wave analysis on the middle spin component of the field. The results hold for a more general class of spherically symmetric spacetimes with the same arguments used in this paper.

math.AP↗
arXiv2017

Reissner-Nordstrøm-de Sitter Manifold : Photon Sphere and Maximal Analytic Extension

This paper is devoted to the study of the Reissner-Nordstrøm-de Sitter black holes and their maximal analytic extensions. In particular, we study some of their properties that lays the groundwork for separate papers where we obtain decay results and construct conformal scattering theories for test fields on such spacetimes. Here, we find the necessary and sufficient conditions on the parameters of the Reissner-Nordstrøm-de Sitter metric -namely, the mass, the charge, and the cosmological constant- to have three horizons. Under this conditions, we prove that there is only one photon sphere and we locate it. We then give a detailed construction of the maximal analytic extension of the Reissner-Nordstrøm-de Sitter manifold in the case of three horizons.

math.DG↗