Scattering theory for the Dirac equation in Schwarzschild–Anti–de Sitter space-time

Idelon-Riton, Guillaume

doi:10.4310/atmp.2018.v22.n4.a3

Cited by 7 publications

(16 citation statements)

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“…Whereas the spectrum of the elliptic part is discrete in the Anti-de Sitter case, it becomes continuous when looking at the Schwarzschild-Anti-de Sitter black hole. Asymptotic completeness for the massive Dirac equation on this last spacetime was shown by the author in [28]. Quasimodes for this same equation were constructed in [27].In this paper, we give an explicit formula for the resolvent of the Dirac operator in the Schwarzschild-Anti-de Sitter spacetime and show that the weighted resolvent extends meromorphically through the real axis, see section 3.…”

mentioning

confidence: 72%

“…We will now work with these coordinates. For more details about how to obtain this form of the equation, we refer to a previous work [28]. Recall that the Dirac matrices γ µ , 0 µ 3, unique up to unitary transform, are given by the following relations:…”

Section: The Dirac Equationmentioning

confidence: 99%

“…where Ys,n span the corresponding spinoidal spherical harmonic for harmonics s and n fixed. It was proven in [28], that this operator is self-adjoint for all positive masses when equipped with the appropriate domain.…”

Section: The Dirac Equationmentioning

confidence: 99%

“…Recall, from [28], that, for 2ml < 1, H s,n m is self-adjoint with domain: 4 . These boundary conditions can be rewritten as:…”

Section: Solutions Satisfying Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Explicit formula and meromorphic extension of the resolvent for the massive Dirac operator in the Schwarzschild-anti-de Sitter spacetime

Idelon-Riton

2017

Journal of Mathematical Physics

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confidence: 72%

Section: The Dirac Equationmentioning

confidence: 99%

Section: The Dirac Equationmentioning

confidence: 99%

“…Recall, from [28], that, for 2ml < 1, H s,n m is self-adjoint with domain: 4 . These boundary conditions can be rewritten as:…”

Section: Solutions Satisfying Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Explicit formula and meromorphic extension of the resolvent for the massive Dirac operator in the Schwarzschild-anti-de Sitter spacetime

Idelon-Riton

2017

Journal of Mathematical Physics

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Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime

Pham

2023

Class. Quantum Grav.

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In this paper, we establish the constructions of conformal scattering theories for the tensorial wave equation such as the tensorial Fackerell-Ipser and the spin $\pm 1$ Teukolsky equations on Schwarzschild spacetime. In our strategy, we construct the conformal scattering for the tensorial Fackerell-Ipser equations which are obtained from the Maxwell equation and spin $\pm 1$ Teukolsky equations. Our method combines Penrose's conformal compactification and the energy decay results of the tensorial fields satisfying the tensorial Fackerell-Ipser equation to prove the energy equality of the fields through the conformal boundary $\mathfrak{H}^+\cup \scri^+$ (resp. $\mathfrak{H}^-\cup \scri^-$) and the initial Cauchy hypersurface $\Sigma_0 = \left\{ t=0 \right\}$. We will prove the well-posedness of the Goursat problem by using a generalization of H"ormander's results for the tensorial wave equations. By using the results for the tensorial Fackerell-Ipser equations we will establish the construction of conformal scattering for the spin $\pm 1$ Teukolsky equations.

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The Well-Posedness of the Cauchy Problem for the Dirac Operator on Globally Hyperbolic Manifolds with Timelike Boundary

Große

Murro

2020

Doc. Math.

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We consider the Dirac operator on globally hyperbolic manifolds with timelike boundary and show well-posedness of the Cauchy initial boundary value problem coupled to MIT-boundary conditions. This is achieved by transforming the problem locally into a symmetric positive hyperbolic system, proving existence and uniqueness of weak solutions and then using local methods developed by Lax, Phillips and Rauch, Massey to show smoothness of the solutions. Our proof actually works for a slightly more general class of local boundary conditions.

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Scattering theory for the Dirac equation in Schwarzschild–Anti–de Sitter space-time

Abstract: We show asymptotic completeness for linear massive Dirac fields on the Schwarzschild-Anti-de Sitter spacetime. The proof is based on a Mourre estimate. We also construct an asymptotic velocity for this field.

Cited by 7 publications

References 43 publications

Explicit formula and meromorphic extension of the resolvent for the massive Dirac operator in the Schwarzschild-anti-de Sitter spacetime

Explicit formula and meromorphic extension of the resolvent for the massive Dirac operator in the Schwarzschild-anti-de Sitter spacetime

Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime

The Well-Posedness of the Cauchy Problem for the Dirac Operator on Globally Hyperbolic Manifolds with Timelike Boundary

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