]. A. Bachelot, Asymptotic completeness for the Klein-Gordon equation on the Schwarzschild metric, Ann. Inst. H. Poincaré Phys. Théor, pp.61-411, 1994.

A. Stud, The Hawking effect, Nonlinear evolutionary partial differential equations, pp.489-493, 1993.

A. Bachelot and A. Motet-bachelot, Les résonances d'un trou noir de Schwarzschild, Ann. Inst. H. Poincaré Phys. Théor, vol.59, pp.3-68, 1993.

J. C. Baez, I. E. Segal, and Z. Zhou, The global Goursat problem and scattering for nonlinear wave equations, Journal of Functional Analysis, vol.93, issue.2, pp.93-239, 1990.
DOI : 10.1016/0022-1236(90)90128-8

A. N. Bernal and M. Sanchez, On Smooth Cauchy Hypersurfaces and Geroch???s Splitting Theorem, Communications in Mathematical Physics, vol.14, issue.3, pp.461-470, 2003.
DOI : 10.1007/s00220-003-0982-6

V. Burenkov, Extension theorems for Sobolev spaces, in The Maz'ya anniversary collection, Theory Adv. Appl, vol.1, issue.109, pp.187-200, 1998.

G. Caciotta and F. Nicoì-o, GLOBAL CHARACTERISTIC PROBLEM FOR EINSTEIN VACUUM EQUATIONS WITH SMALL INITIAL DATA: (I) THE INITIAL DATA CONSTRAINTS, Journal of Hyperbolic Differential Equations, vol.02, issue.01, pp.201-277, 2005.
DOI : 10.1142/S0219891605000439

F. Cagnac and Y. Choquet-bruhat, Solution globale d'uné equation non linéaire sur une variété hyperbolique, J. Math. Pures Appl, issue.9, pp.63-377, 1984.

J. Cheeger and D. G. Ebin, Comparison theorems in Riemannian geometry, 1975.
DOI : 10.1090/chel/365

Y. Choquet-bruhat, Global existence for solutions of u = a|u| p, General relativity and the Einstein equations, pp.98-108, 1989.

D. Christodoulou, H. Müller, and . Hagen, Probì eme de valeur initiale caractéristique pour des systèmes quasi linéaires du second ordre, C. R. Acad. Sci. Paris Sér. I Math, vol.293, pp.39-42, 1981.

P. T. Chru´scielchru´sciel, E. Delay, and . Erratum, Existence of non-trivial, vacuum, asymptotically simple spacetimes, Classical Quantum Gravity, vol.19, p.3389, 2002.

P. T. Chru´scielchru´sciel and E. Delay, Existence of non-trivial, vacuum, asymptotically simple spacetimes, Classical and Quantum Gravity, vol.19, issue.9, pp.71-79, 2002.
DOI : 10.1088/0264-9381/19/9/101

P. T. Chru´scielchru´sciel and J. Shatah, Global existence of solutions of the Yang-Mills equations on a globally hyperbolic four dimensional lorentzian manifolds, Asian, J. Math, vol.1, pp.530-548, 1997.

J. Corvino, Scalar Curvature Deformation and a Gluing Construction for the Einstein Constraint Equations, Communications in Mathematical Physics, vol.214, issue.1, pp.137-189, 2000.
DOI : 10.1007/PL00005533

J. Corvino and R. M. Schoen, On the Asymptotics for the Vacuum Einstein Constraint Equations, Journal of Differential Geometry, vol.73, issue.2, pp.185-217, 2006.
DOI : 10.4310/jdg/1146169910

M. Dafermos and I. Rodnianski, The red-shift effect and radiation decay on black hole spacetimes, Communications on Pure and Applied Mathematics, vol.53, issue.5, pp.859-919, 2009.
DOI : 10.1002/cpa.20281

T. Daudé, Estimations de propagation pour des op??rateurs de Dirac et application ?? la th??orie de la diffusion, Annales de l???institut Fourier, vol.54, issue.6, pp.2021-2083, 2004.
DOI : 10.5802/aif.2074

J. Dimock, Dirac quantum fields on a manifold, Transactions of the American Mathematical Society, vol.269, issue.1, pp.133-147, 1982.
DOI : 10.1090/S0002-9947-1982-0637032-8

J. Dimock and B. S. Kay, Classical and quantum scattering theory for linear scalar fields on the Schwarzschild metric. II, Journal of Mathematical Physics, vol.27, issue.10, pp.2520-2525, 1986.
DOI : 10.1063/1.527319

M. Dossa, Solutions C ? d'une classe deprobì emes de Cauchy quasi-linéaires hyperboliques du second ordre sur un cono¨?decono¨?de caractéristique, Ann. Fac. Sci. Toulouse Math, issue.6, pp.11-351, 2002.

M. Dossa and F. Touadera, Solutions globales de syst??mes hyperboliques non lin??aires sur un c??ne caract??ristique, Comptes Rendus Mathematique, vol.341, issue.7, pp.341-409, 2005.
DOI : 10.1016/j.crma.2005.09.002

J. J. Duistermaat and L. Hörmander, Fourier integral operators ii, Acta Math, vol.128, pp.182-269, 1972.
DOI : 10.1007/978-3-662-03030-1_3

D. M. Eardley and V. Moncrief, The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space, Communications in Mathematical Physics, vol.139, issue.2, pp.171-191, 1982.
DOI : 10.1007/BF01976040

J. Ehlers, Foundations of Gravitational Lens Theory (Geometry of Light Cones), Annalen der Physik, vol.292, issue.3-5, pp.307-320, 2000.
DOI : 10.1002/(SICI)1521-3889(200005)9:3/5<307::AID-ANDP307>3.0.CO;2-H

J. Ehlers and E. T. Newman, The theory of caustics and wave front singularities with physical applications, Journal of Mathematical Physics, vol.41, issue.6, pp.3344-3378, 2000.
DOI : 10.1063/1.533316

J. Frauendiener and H. Friedrich, The conformal structure of space-time : geometry , analysis, numerics, 2002.
DOI : 10.1007/3-540-45818-2

J. Frauendiener and G. A. Sparling, On a class of consistent linear higher spin equations on curved manifolds, Journal of Geometry and Physics, vol.30, issue.1, pp.54-101, 1999.
DOI : 10.1016/S0393-0440(98)00050-3

F. Friedlander, Notes on the Wave Equation on Asymptotically Euclidean Manifolds, Journal of Functional Analysis, vol.184, issue.1, pp.1-18, 2001.
DOI : 10.1006/jfan.2000.3546

F. G. Friedlander, Radiation fields and hyperbolic scattering theory, Mathematical Proceedings of the Cambridge Philosophical Society, vol.87, issue.03, pp.483-515, 1980.
DOI : 10.1512/iumj.1972.22.22022

S. Frittelli, E. T. Newman, and G. Silva-ortigoza, Conjugate points along null geodesics of asymptotically flat spacetimes, Classical and Quantum Gravity, vol.15, issue.3, pp.689-703, 1998.
DOI : 10.1088/0264-9381/15/3/017

L. Garding, T. Kotake, and J. Leray, Uniformisation et développement asymptotique de la solution duprobì eme de cauchy linéairè a données holomorphes; analogie avec la théorie des ondes asymptotiques et approchées, Bull. S.M.F, p.92, 1964.

R. Geroch, Spinor Structure of Space???Times in General Relativity. I, Journal of Mathematical Physics, vol.9, issue.11, pp.1739-1744, 1968.
DOI : 10.1063/1.1664507

P. Günther, Huygens' principle and hyperbolic equations, 1988.

D. Häfner, Sur la théorie de la diffusion pour l'´ equation de Klein-Gordon dans la métrique de Kerr, Dissertationes Math. (Rozprawy Mat, pp.421-102, 2003.

D. Häfner and J. Nicolas, The characteristic Cauchy problem for Dirac fields on curved backgrounds

E. Hebey, Nonlinear analysis on manifolds: Sobolev spaces and inequalities, Courant Lecture Notes in Mathematics, vol.5, 1999.
DOI : 10.1090/cln/005

L. Hörmander, Fourier integral operators. I, Acta Math, pp.79-183, 1971.

D. E. Houpa and M. Dossa, Probì emes de Goursat pour des systèmes semi-linéaires hyperboliques, C. R. Math. Acad. Sci. Paris, pp.341-356, 2005.

J. Joudioux, Integral formula for the characteristic Cauchy problem on a curved background, Journal de Math??matiques Pures et Appliqu??es, vol.95, issue.2, 2009.
DOI : 10.1016/j.matpur.2010.10.002
URL : https://hal.archives-ouvertes.fr/hal-00426219

D. M. Kerrick, A comment on the generalized Kirchhoff???d???Adh??mar formula for massless free fields in Minkowski space???time, Journal of Mathematical Physics, vol.33, issue.3, pp.974-976, 1992.
DOI : 10.1063/1.529750

S. Klainerman and F. Nicoì-o, On local and global aspects of the Cauchy problem in general relativity, Classical and Quantum Gravity, vol.16, issue.8, pp.73-157, 1999.
DOI : 10.1088/0264-9381/16/8/201

S. Klainerman, I. Rodnianski, and . Kirchoff, A KIRCHOFF???SOBOLEV PARAMETRIX FOR THE WAVE EQUATION AND APPLICATIONS, Journal of Hyperbolic Differential Equations, vol.04, issue.03, pp.401-433, 2007.
DOI : 10.1142/S0219891607001203

H. B. Lawson and M. Michelsohn, Spin geometry, 1989.

L. Mason and J. Nicolas, CONFORMAL SCATTERING AND THE GOURSAT PROBLEM, Journal of Hyperbolic Differential Equations, vol.01, issue.02, pp.197-233, 2004.
DOI : 10.1142/S0219891604000123

F. Melnyk, Scattering on Reissner-Nordstr??m Metric for Massive Charged Spin 1/2 Fields, Annales Henri Poincar??, vol.4, issue.5, pp.813-846, 2003.
DOI : 10.1007/s00023-003-0148-2

V. Moncrief, Analytic reductions of self-force calculations in curved spacetimes, Classical and Quantum Gravity, vol.23, issue.16, pp.463-475, 2006.
DOI : 10.1088/0264-9381/23/16/S10

C. S. Morawetz, The decay of solutions of the exterior initial-boundary value problem for the wave equation, Communications on Pure and Applied Mathematics, vol.3, issue.3, pp.561-568, 1961.
DOI : 10.1002/cpa.3160140327

H. Müller and . Hagen, Characteristic initial value problem for hyperbolic systems of second order differential equations, Ann. Inst. H. Poincaré Phys. Théor, pp.53-159, 1990.

H. Müller-zum-hagen and H. Seifert, On characteristic initial-value and mixed problems, General Relativity and Gravitation, vol.14, issue.4, pp.259-301, 1977.
DOI : 10.1007/BF00765812

J. Nicolas and L. , ´ equation linéaire de Klein-Gordon et le système linéaire de Dirac en métrique de type Schwarzschild 1, ´ Ecole doctoral de mathématiques, 1994. [70] , Global exterior problem for spin 3/2 zero rest-mass fields in the schwarzschild space-time, Comm. in P.D.E, pp.22-465, 1997.

F. Nicoì-o, The characteristic problem for the Einstein vacuum equations, Nuovo Cimento Soc. Ital. Fis. B, vol.119, pp.749-771, 2004.

P. Nurowski and D. C. Robinson, Intrinsic geometry of a null hypersurface, Classical and Quantum Gravity, vol.17, issue.19, pp.4065-4084, 2000.
DOI : 10.1088/0264-9381/17/19/308

J. T. Ottesen, The dirac equation with light-cone data, Reports on Mathematical Physics, vol.27, issue.3, pp.287-297, 1989.
DOI : 10.1016/0034-4877(89)90012-8

R. Penrose, Zero Rest-Mass Fields Including Gravitation: Asymptotic Behaviour, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.284, issue.1397, pp.159-203, 1965.
DOI : 10.1098/rspa.1965.0058

R. Penrose, Golden Oldie, General Relativity and Gravitation, vol.248, issue.3, pp.225-264, 1963.
DOI : 10.1007/BF00756234

R. Penrose and W. Rindler, Spinors and Space-time I & II, 1986.

S. Seitz, P. Schneider, and J. Ehlers, Light propagation in arbitrary spacetimes and the gravitational lens approximation, Classical and Quantum Gravity, vol.11, issue.9, pp.2345-2373, 1994.
DOI : 10.1088/0264-9381/11/9/016

E. M. Stein, Singular integrals and differentiability properties of functions, 1970.

M. E. Taylor, Partial differential equations. I, of Applied Mathematical Sciences, 1996.