Conformal scattering theory for the linearized gravity fields on Schwarzschild spacetime

Pham, Truong Xuan

doi:10.1007/s10455-021-09789-y

Cited by 3 publications

(14 citation statements)

References 25 publications

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“…The result of Hörmander was extended for the scalar wave equation by Nicolas [19] with the following minor modifications: the C 1 -metric, the continuous coefficients of the derivatives of the first order and the terms of order zero have locally L ∞ -coefficients. We refer [6,15,21,24] for…”

Section: Appendix Amentioning

confidence: 99%

“…The Goursat problem is an important step to construct the conformal scattering theory for the field equations in the asymptotic simple and flat spacetimes (in detail see [10,21] for the construction of the theory). In related work, the wellposedness of the Goursat problem and conformal scattering theories for the Regge-Wheeler and Zerilli equations in Schwarzschild spacetime have been obtained by Pham [24].…”

Section: Introductionmentioning

confidence: 99%

“…We develop the methods in [10,15,21,24] to establish the wellposedness of the Goursat problem. In particular, the Goursat problem will be considered in the partial conformal compactification spacetime in two parts.…”

Section: Introductionmentioning

confidence: 99%

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Cauchy and Goursat problems for the generalized spin zero rest-mass equations on Minkowski spacetime

Xuan¹

2022

Class. Quantum Grav.

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In this paper, we study the Cauchy and Goursat problems of the spin-$n/2$ zero rest-mass equations on Minkowski spacetime by using the conformal geometric method. In our strategy, we prove the wellposedness of the Cauchy problem in Einstein's cylinder. Then we establish pointwise decays of the fields and prove the energy equalities of the conformal fields between the null conformal boundaries $\scri^\pm$ and the hypersurface $\Sigma_0=\left\{ t=0 \right\}$. Finally, we prove the wellposedness of the Goursat problem in the partial conformal compactification by using the energy equalities and the generalisation of H\"ormander's result.

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Section: Appendix Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Cauchy and Goursat problems for the generalized spin zero rest-mass equations on Minkowski spacetime

Xuan¹

2022

Class. Quantum Grav.

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“…In particular, the conformal scattering theory (i.e. the geometric scattering theory) has been studied extensively from the early works by Friedlander [25][26][27][28][29], Baez et al [8], Hörmander [37] to recent ones by Mason and Nicolas [49], Joudioux [41,42], Nicolas [59], Mokdad [53,54], Taujanskas [72] and Pham [63,65].…”

Section: Introductionmentioning

confidence: 99%

“…Continuing this program, Mokdad [53,54] constructed explicitly the conformal scattering theories for the Maxwell and Dirac equations on the static exterior and dynamic interior of Reissner-Nordström de Sitter spacetimes, respectively. On the other hand, Pham [63] constructed conformal scattering theories for the scalar Reeger-Wheeler and Zerelli equations arising from the linearized gravity fields and the spin ±2 Teukolsky equations. This is the first step to obtain the conformal scattering theory for the linearized gravity fields on the Schwarzschild spacetime which is spherical symmetric.…”

Section: Introductionmentioning

confidence: 99%

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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Conformal Scattering Theory for the Dirac Equation on Kerr Spacetime

Pham

2022

Ann. Henri Poincaré

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Conformal scattering theory for the linearized gravity fields on Schwarzschild spacetime

Cited by 3 publications

References 25 publications

Cauchy and Goursat problems for the generalized spin zero rest-mass equations on Minkowski spacetime

Cauchy and Goursat problems for the generalized spin zero rest-mass equations on Minkowski spacetime

Conformal scattering theories for tensorial wave equations on Schwarzschild spacetime

Conformal Scattering Theory for the Dirac Equation on Kerr Spacetime

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