no. 5
Conformal Scattering of Maxwell fields on Reissner–Nordström–de Sitter Black Hole Spacetimes
Annales de l'Institut Fourier, Volume 69 (2019) no. 5, pp. 2291-2329.

We construct a complete conformal scattering theory for Maxwell fields in the static exterior region of a Reissner–Nordström–de Sitter black hole spacetime. We use uniform energy decay results, which 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.

Nous construisons une théorie complète de scattering conforme pour les champs de Maxwell dans l’extérieur statique de l’espace-temps de trou noir de De Sitter–Reissner–Nordström. Nous utilisons des résultats de décroissance que nous avons obtenus dans un article séparé, afin de montrer que les opérateurs de trace sont injectifs et d’images fermées. Ensuite, nous résolvons le problème de Goursat pour les champs de Maxwell sur la frontière isotrope ce qui montre que les opérateurs de trace sont surjectifs aussi.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3295
Classification: 35Q61,  35P25,  35Q75,  83C57,  83C50
Keywords: Conformal scattering, Black holes, Maxwell’s equations, Reissner–Nordström–de Sitter metric, Goursat problem 
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     title = {Conformal {Scattering} of {Maxwell} fields on {Reissner{\textendash}Nordstr\"om{\textendash}de} {Sitter} {Black} {Hole} {Spacetimes}},
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Mokdad, Mokdad. Conformal Scattering of Maxwell fields on Reissner–Nordström–de Sitter Black Hole Spacetimes. Annales de l'Institut Fourier, Volume 69 (2019) no. 5, pp. 2291-2329. doi : 10.5802/aif.3295. https://aif.centre-mersenne.org/articles/10.5802/aif.3295/

[1] Bachelot, Alain Gravitational scattering of electromagnetic field by Schwarzschild black-hole, Annales de l’I.H.P. Physique théorique, Tome 54 (1991) no. 3, pp. 261-320 | MR: 1122656 | Zbl: 0743.53037

[2] Chrusciel, Piotr T.; Delay, Erwann Existence of non-trivial, vacuum, asymptotically simple spacetimes, Class. Quant. Grav., Tome 19 (2002) no. 9, L71 pages | MR: 1902228 | Zbl: 1005.83009

[3] Chrusciel, Piotr T.; Delay, Erwann On mapping properties of the general relativistic constraints operator in weighted function spaces, with applications, Mem. Soc. Math. France, Tome 94 (2003), pp. 1-103 | Zbl: 1058.83007

[4] Corvino, Justin Scalar curvature deformation and a gluing construction for the Einstein constraint equations, Commun. Math. Phys., Tome 214 (2000) no. 1, pp. 137-189 | MR: 1794269 | Zbl: 1031.53064

[5] Corvino, Justin; Schoen, Richard M. On the asymptotics for the vacuum Einstein constraint equations, J. Differ. Geom., Tome 73 (2006) no. 2, pp. 185-217 | MR: 2225517 | Zbl: 1122.58016

[6] Dafermos, Mihalis; Rodnianski, Igor Lectures on black holes and linear waves, Evolution equations (Clay Mathematics Proceedings) Tome 17, Clay Mathematics Institute, 2008, pp. 97-205 | Zbl: 1300.83004

[7] Friedlander, F. Gerard On the radiation field of pulse solutions of the wave equation, Proc. R. Soc. Lond., Ser. A, Tome 269 (1962), pp. 53-65 | MR: 142888 | Zbl: 0106.41501

[8] Friedlander, F. Gerard On the radiation field of pulse solutions of the wave equation. II, Proc. R. Soc. Lond., Ser. A, Tome 279 (1964), pp. 386-394 | MR: 164132 | Zbl: 0117.43904

[9] Friedlander, F. Gerard On the radiation field of pulse solutions of the wave equation. III, Proc. R. Soc. Lond., Ser. A, Tome 299 (1967), pp. 264-278 | MR: 226218 | Zbl: 0163.23702

[10] Friedlander, F. Gerard Radiation fields and hyperbolic scattering theory, Math. Proc. Camb. Philos. Soc., Tome 88 (1980), pp. 483-515 | Article | MR: 583989 | Zbl: 0465.35098

[11] Hörmander, Lars A remark on the characteristic Cauchy problem, J. Funct. Anal., Tome 93 (1990) no. 2, pp. 270-277 | Article | MR: 1073287 | Zbl: 0724.35060

[12] Joudioux, Jérémie Problème de Cauchy caractéristique et scattering conforme en relativité générale (2010) (Ph. D. Thesis)

[13] Joudioux, Jérémie Conformal scattering for a nonlinear wave equation, J. Hyperbolic Differ. Equ., Tome 09 (2012) no. 01, pp. 1-65 | Article | MR: 2910977 | Zbl: 1246.83063

[14] Leray, Jean Hyperbolic differential equations, Institute for advanced study, 1955 | Zbl: 0067.07301

[15] Mason, Lionel J.; Nicolas, Jean-Philippe Conformal scattering and the goursat problem, J. Hyperbolic Differ. Equ., Tome 01 (2004) no. 02, pp. 197-233 | Article | MR: 2070126 | Zbl: 1074.83019

[16] Mason, Lionel J.; Nicolas, Jean-Philippe Regularity at space-like and null infinity, J. Inst. Math. Jussieu, Tome 8 (2009) no. 01, pp. 179-208 | Article | MR: 2461904 | Zbl: 1160.35348

[17] Mokdad, Mokdad Maxwell Field on the Reissner–Nordström–de Sitter Manifold: Decay and Conformal Scattering (2016) (Ph. D. Thesis)

[18] Mokdad, Mokdad Decay of Maxwell Fields on Reissner–Nordström–de Sitter Black Holes (2017) (http://arxiv.org/abs/1704.06441) | Zbl: 1372.83048

[19] Mokdad, Mokdad Reissner–Nordström–de Sitter manifold: photon sphere and maximal analytic extension, Class. Quantum Grav., Tome 34 (2017) no. 17, 175014, 175014 pages | Article | MR: 3687806 | Zbl: 1372.83048

[20] Nicolas, Jean-Philippe Conformal scattering on the Schwarzschild metric, Ann. Inst. Fourier, Tome 66 (2016) no. 3, pp. 1175-1216 | Article | MR: 3494169 | Zbl: 1373.35050

[21] Penrose, Roger Asymptotic Properties of Fields and Space-Times, Phys. Rev. Lett., Tome 10 (1963) no. 2, pp. 66-68 | Article | MR: 149912

[22] Penrose, Roger Conformal treatment of infinity, Relativité, Groupes et Topologie (Lectures, Les Houches, 1963 Summer School of Theoret. Phys., Univ. Grenoble), Gordon and Breach, New York, 1964, pp. 565-584 | Zbl: 0148.46403

[23] Penrose, Roger Zero rest-mass fields including gravitation: asymptotic behaviour, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, Tome 284 (1965) no. 1397, pp. 159-203 | Article | MR: 175590 | Zbl: 0129.41202

[24] Penrose, Roger; Rindler, Wolfgang Spinors and space-time: Volume 1, Two-spinor calculus and relativistic fields Tome 1, Cambridge University Press, 1987 | Zbl: 0663.53013

[25] Penrose, Roger; Rindler, Wolfgang Spinors and space-time: Volume 2, Spinor and twistor methods in space-time geometry Tome 2, Cambridge University Press, 1988 | Zbl: 0591.53002

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