zbMATH — the first resource for mathematics

The extended conformal Einstein field equations with matter: the Einstein-Maxwell field. (English) Zbl 1239.53018
Summary: A discussion is given of the conformal Einstein field equations coupled with matter whose energy-momentum tensor is trace-free. The resulting equations are expressed in terms of a generic Weyl connection. The article shows how in the presence of matter it is possible to construct a conformal gauge which allows to know a priori the location of the conformal boundary. In vacuum this gauge reduces to the so-called conformal Gaussian gauge. These ideas are applied to obtain (i) a new proof of the stability of Einstein-Maxwell de Sitter-like space-times; (ii) a proof of the semi-global stability of purely radiative Einstein-Maxwell space-times.

53B30 Local differential geometry of Lorentz metrics, indefinite metrics
83C22 Einstein-Maxwell equations
Full Text: DOI arXiv
[1] Friedrich, H., On the existence of \(n\)-geodesically complete or future complete solutions of einstein’s field equations with smooth asymptotic structure, Comm. math. phys., 107, 587, (1986) · Zbl 0659.53056
[2] Friedrich, H., On the global existence and the asymptotic behaviour of solutions to the einstein – maxwell – yang – mills equations, J. differential geom., 34, 275, (1991) · Zbl 0737.53070
[3] Friedrich, H., Einstein equations and conformal structure: existence of anti-de Sitter-type space – times, J. geom. phys., 17, 125, (1995) · Zbl 0840.53055
[4] Friedrich, H., Conformal Einstein evolution, (), 1 · Zbl 1054.83006
[5] Friedrich, H., Conformal geodesics on vacuum spacetimes, Comm. math. phys., 235, 513, (2003) · Zbl 1040.53079
[6] Friedrich, H., Gravitational fields near space-like and null infinity, J. geom. phys., 24, 83, (1998) · Zbl 0896.53053
[7] Lübbe, C.; Valiente Kroon, J.A., On de Sitter-like and Minkowski-like spacetimes, Classical quantum gravity, 26, 145012, (2009) · Zbl 1172.83008
[8] Lübbe, C.; Valiente Kroon, J.A., A stability result for purely radiative spacetimes, J. hyperbolic differ. equ., 7, 545, (2010) · Zbl 1204.83015
[9] Penrose, R.; Rindler, W., ()
[10] 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. lond. ser. A, 378, 401, (1981) · Zbl 0481.58026
[11] Friedrich, H., On the regular and the asymptotic characteristic initial value problem for einstein’s vacuum field equations, Proc. R. soc. lond. ser. A, 375, 169, (1981) · Zbl 0454.58017
[12] Friedrich, H., Cauchy problems for the conformal vacuum field equations in general relativity, Comm. math. phys., 91, 445, (1983) · Zbl 0555.35116
[13] Sommers, P., Space spinors, J. math. phys., 21, 2567, (1980)
[14] Kato, T., Linear evolution equations of “hyperbolic” type, J. fac. sci. univ. Tokyo, 17, 241, (1970) · Zbl 0222.47011
[15] Kato, T., Linear evolution equations of “hyperbolic” type. II, J. math. soc. Japan, 25, 648, (1973) · Zbl 0262.34048
[16] Kato, T., The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. ration. mech. anal., 58, 181, (1975) · Zbl 0343.35056
[17] Simon, W., Radiative einstein – maxwell spacetimes and ‘no hair’ theorems, Classical quantum gravity, 9, 241, (1992) · Zbl 0747.53067
[18] Friedrich, H., On static and radiative space – times, Comm. math. phys., 119, 51, (1988) · Zbl 0658.53074
[19] Newman, E.T.; Penrose, R., 10 exact gravitationally-conserved quantities, Phys. rev. lett., 15, 231, (1965)
[20] Newman, E.T.; Penrose, R., New conservation laws for zero rest-mass fields in asymptotically flat space – time, Proc. R. soc. lond. ser. A, 305, 175, (1968)
[21] Exton, A.R.; Newman, E.T.; Penrose, R., Conserved quantities in the einstein – maxwell theory, J. math. phys., 10, 1566, (1969)
[22] Friedrich, H.; Schmidt, B., Conformal geodesics in general relativity, Proc. R. soc. lond. ser. A, 414, 171, (1987) · Zbl 0629.53063
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.