 |
1 |
Abrahams, A., Anderson, A., Choquet-Bruhat, Y., and York Jr, J.W., “A nonstrictly hyperbolic
system for the Einstein equations with arbitrary lapse and shift”, C. R. Acad. Sci. Ser. II, 323,
835–841, (1996). [ gr-qc/9607006].
|
 |
2 |
Abrahams, A.M., Anderson, A., Choquet-Bruhat, Y., and York Jr, J.W., “Einstein and
Yang–Mills theories in hyperbolic form without gauge fixing”, Phys. Rev. Lett., 75, 3377–3381,
(1996). [ gr-qc/9506072].
|
 |
3 |
Abrahams, A.M., Anderson, A., Choquet-Bruhat, Y., and York Jr, J.W., “Geometrical
hyperbolic systems for general relativity and gauge”, Class. Quantum Grav., 14, A9–A22, (1997).
[ gr-qc/9605014].
|
 |
4 |
Abrahams, A.M., Anderson, A., Choquet-Bruhat, Y., and York Jr, J.W., “Hyperbolic
Formulation of General Relativity”, arXiv e-print, (1997). [ gr-qc/9703010].
|
 |
5 |
Alcubierre, M., “Appearance of coordinate shocks in hyperbolic formalisms of general relativity”,
Phys. Rev. D, 55, 5981–5991, (1997).
|
 |
6 |
Alcubierre, M., and Massó, J., “Pathologies of hyperbolic gauges in general relativity and other
field theories”, Phys. Rev. D, 57, R4511–R4515, (1998). [ gr-qc/9709024].
|
 |
7 |
Ashtekar, A., “New Hamiltonian Formulation of General Relativity”, Phys. Rev. D, 36(6),
1587–1602, (1987).
|
 |
8 |
Ashtekar, A., New Perspectives in Canonical Gravity, (Bibliopolis, Naples, 1988).
|
 |
9 |
Bona, C., and Massó, J., “Hyperbolic evolution system for numerical relativity”, Phys. Rev.
Lett., 68, 1097–1099, (1992).
|
 |
10 |
Bona, C., Massó, J., Seidel, E., and Stela, J., “New Formalism for Numerical Relativity”, Phys.
Rev. Lett., 75, 600–603, (1995). [ gr-qc/9412071].
|
 |
11 |
Bona, C., Massó, J., Seidel, E., and Stela, J., “First order hyperbolic formalism for numerical
relativity”, Phys. Rev. D, 56, 3405–3415, (1997). [ gr-qc/9709016].
|
 |
12 |
Bona, C., Massó, J., and Stela, J., “Numerical black holes: a moving grid approach”, Phys.
Rev. D, 51, 1639–1645, (1995). [ gr-qc/9412070].
|
 |
13 |
Bruhat, Y., “Théorème d’existence pour certains systèmes d’équations aux dérivées
partielles non linéaires”, Acta Math., 88, 141–225, (1952).
|
 |
14 |
Bruhat, Y., “Un théorème d’inestabilité pour certain équations hyperboliques
nonlinéaires”, C. R. Acad. Sci., 276A, 281, (1973).
|
 |
15 |
Choquet-Bruhat, Y., “Espaces temps eineiniens généraux, chocs gravitationnels”, Ann. Inst.
Henri Poincare, 8, 327–338, (1968).
|
 |
16 |
Choquet-Bruhat, Y., and Christodoulou, D., “Elliptic systems in Hs,δ spaces on manifolds which
are Euclidean at infinity”, Acta Math., 145, 129–150, (1981).
|
 |
17 |
Choquet-Bruhat, Y., Christodoulou, D., and Francaviglia, M., “Cauchy data on a manifold”,
Ann. Inst. Henri Poincare A, 29, 241–255, (1978).
|
 |
18 |
Choquet-Bruhat, Y., and Ruggeri, T., “Hyperbolicity of the 3+1 System of Einstein Equations”,
Commun. Math. Phys., 89, 269–275, (1983).
|
 |
19 |
Choquet-Bruhat, Y., and York Jr, J.W., “Mixed elliptic and hyperbolic system for the Einstein
equations”, in Ferrarese, G., ed., Gravitation, Electromagnetism and Geometric Structures,
International Conference in honour of A. Lichnerowicz, Villa Tuscolana, 19 – 23 October 1995,
(Pitagora, Bologna, 1996). [ gr-qc/9601030].
|
 |
20 |
Christodoulou, D., and Klainerman, S., The Global Nonlinear Stability of the Minkowski Space,
Princeton Mathematical Series, vol. 41, (Princeton University Press, Princeton, 1993).
|
 |
21 |
Christodoulou, D., and Ó Murchadha, N., “The boost problem in general relativity”, Commun.
Math. Phys., 80, 271–300, (1981).
|
 |
22 |
Cutler, C., and Wald, R.M., “Existence of radiating Einstein–Maxwell solutions which are C∞
on all of I− and I+”, Class. Quantum Grav., 6, 453–466, (1989).
|
 |
23 |
DeTurk, D., “The Cauchy problem for Lorentz metrics with prescribed Ricci curvature”, Comp.
Math., 48, 327–349, (1983).
|
 |
24 |
Fischer, A., and Marsden, J., “The Einstein Evolution Equations as a First-Order Symmetric
Hyperbolic Quasilinear System”, Commun. Math. Phys., 28, 1–38, (1972).
|
 |
25 |
Fischer, A., and Marsden, J., “General relativity, partial differential equations, and dynamical
systems”, in Spencer, D.C., ed., Partial Differential Equations, Proceedings of Symposia in Pure
Mathematics, vol. 23, pp. 309–327, (AMS, Providence, 1973).
|
 |
26 |
Friedrich, H., “The Asymptotic Characteristic Initial Value Problem for Einstein’s Vacuum Field
Equations as an Initial Value Problem for a First-Order Quasilinear Symmetric Hyperbolic
System”, Proc. R. Soc. London, Ser. A, 378, 401–421, (1981). [ DOI], [ ADS].
|
 |
27 |
Friedrich, H., “On the regular and the asymptotic characteristic initial value problem for
Einstein’s vacuum field equations”, Proc. R. Soc. London, Ser. A, 375, 169–184, (1981). [ ADS].
|
 |
28 |
Friedrich, H., “On the hyperbolicity of Einstein’s and other gauge field equations”, Commun.
Math. Phys., 100, 525–543, (1985). [ DOI].
|
 |
29 |
Friedrich, H., “Hyperbolic reductions for Einstein’s equations”, Class. Quantum Grav., 13,
1451–1469, (1996). [ DOI], [ ADS].
|
 |
30 |
Fritelli, S., and Reula, O.A., “On the Newtonian limit of general relativity”, Commun. Math.
Phys., 166, 221–235, (1994). [ gr-qc/9506077].
|
 |
31 |
Frittelli, S., “Note on the propagation of the constraints in standard 3+1 general relativity”,
Phys. Rev. D, 55, 5992–5996, (1997).
|
 |
32 |
Frittelli, S., and Reula, O.A., “First-order symmetric-hyperbolic Einstein equations with
arbitrary fixed gauge”, Phys. Rev. Lett., 76, 4667–4670, (1996). [ gr-qc/9605005].
|
 |
33 |
Geroch, R., “The Local Nonsingularity Theorem”, J. Math. Phys., 24(7), 1851–1858, (1983).
|
 |
34 |
Geroch, R., “Partial Differential Equations of Physics”, arXiv e-print, (1996). [ gr-qc/9602055].
Scottish Summer School in Theoretical Physics.
|
 |
35 |
Geroch, R., and Xanthopolous, B.C., “Asymptotic Simplicity Is Stable”, J. Math. Phys., 19,
714–719, (1978).
|
 |
36 |
Gustafsson, B., Kreiss, H.-O., and Oliger, J., Time Dependent Problems and Difference Methods,
(Wiley, New York, 1995).
|
 |
37 |
Hadamard, J., Lectures on Cauchy’s Problem in Linear Partial Differential Equations, (Yale
University Press, New Haven, 1923).
|
 |
38 |
Hawking, S.W., and Ellis, G.F.R., The Large Scale Structure of Space-Time, Cambridge
Monographs on Mathematical Physics, (Cambridge University Press, Cambridge, 1973).
|
 |
39 |
Hughes, T., Kato, T., and Marsden, J., “Well-posed quasi-linear second order hyperbolic systems
with applications to nonlinear elastodynamics and general relativity”, Arch. Ration. Mech.
Anal., 63, 273–294, (1976).
|
 |
40 |
Iriondo, M.S., Leguizamón, E.O., and Reula, O.A., “Einstein’s equations in Ashtekar
variables constitute a symmetric hyperbolic system”, Phys. Rev. Lett., 79, 4732–4735, (1997).
[ gr-qc/9710004].
|
 |
41 |
Iriondo, M.S., Leguizamón, E.O., and Reula, O.A., “The Newtonian Limit on Asymptotically
Null Foliations”, arXiv e-print, (1997). [ gr-qc/9710003].
|
 |
42 |
Iriondo, M.S., Leguizamón, E.O., and Reula, O.A., “Fast and slow solutions in General
Relativity: The initialization procedure”, J. Math. Phys., 39, 1555–1565, (1998). [ gr-qc/9709078].
|
 |
43 |
John, F., “Formation of Singularities in Elastic Waves”, in Ciarlet, P.G., and Roseau, M., eds.,
Trends and Applications of Pure Mathematics to Mechanics, Invited and Contributed Papers
presented at a Symposium at École Polytechnique, Palaiseau, France, November 28 – December
2, 1983, Lecture Notes in Physics, vol. 195, pp. 194–210, (Springer, Berlin, 1984).
|
 |
44 |
Klainerman, S., “Uniform decay estimates and the Lorentz invariance of the classical wave
equation”, Commun. Pure Appl. Math., 38, 321–332, (1985).
|
 |
45 |
Klainerman, S., “The null condition and global existence to nonlinear wave equations”, Lect.
Appl. Math., 23, 293–326, (1986).
|
 |
46 |
Klainerman, S., “Remarks on the global Sobolev inequalities in Minkowski Space”, Commun.
Pure Appl. Math., 40, 111–117, (1987).
|
 |
47 |
Kreiss, H.-O., “Über sachgemässe Cauchyprobleme”, Math. Scand., 7, 71–80, (1959).
|
 |
48 |
Kreiss, H.-O., and Lorentz, J., Initial-Boundary Value Problems and the Navier–Stokes
Equations, Pure and Applied Mathematics, vol. 136, (Academy Press, Boston, 1989).
|
 |
49 |
Kreiss, H.-O., Nagy, G.B., Ortiz, O.E., and Reula, O.A., “Global existence and exponential decay
for hyperbolic dissipative relativistic fluid theories”, J. Math. Phys., 38, 5272–5279, (1997).
[ ADS].
|
 |
50 |
Leray, J., Hyperbolic Differential Equations, (Institute for Advanced Studies, Princeton, 1953).
|
 |
51 |
Leray, J., and Ohya, Y., “Equations et Systèmes Non-Linéaires hyperboliques non-stricts”,
Math. Ann., 170, 167–205, (1967).
|
 |
52 |
Rendall, A.D., “The Newtonian limit for asymptotically flat solutions of the Vlasov–Einstein
system”, Commun. Math. Phys., 163, 89–112, (1994). [ gr-qc/9303027].
|
 |
53 |
Sideris, T., “Formation of Singularities in 3-d Compressible Fluids”, Commun. Math. Phys.,
101, 475–485, (1985).
|
 |
54 |
Taylor, M.E., Pseudodifferential Operators and Nonlinear PDE, Progress in Mathematics, vol.
100, (Birkhäuser, Boston, 1991).
|
 |
55 |
van Putten, M.H.P.M., and Eardley, D.M., “Nonlinear wave equations for relativity”, Phys. Rev.
D, 53, 3056–3063, (1996). [ gr-qc/9505023].
|
 |
56 |
Wald, R.M., General Relativity, (University of Chicago Press, Chicago, 1984).
|