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Local linearization stability. (English) Zbl 0629.53064
Consider a compact coordinate patch, V, with given “background” metric, \(g_ 0\), solving the vacuum Einstein equations. Let h be a solution of the linearized Einstein equations about \(g_ 0\) in V. Then the Einstein equations are said to be locally linearization stable at \(g_ 0\) if there exists a one parameter family of metrics g(\(\lambda)\) solving the Einstein equations on V such that \(h=dg/d\lambda\) at \(\lambda =0\). This paper proves the existence theorem which establishes local linearization stability about any such \(g_ 0\).
Reviewer: C.Brans

53B50 Applications of local differential geometry to the sciences
35Q99 Partial differential equations of mathematical physics and other areas of application
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
Full Text: DOI
[1] DOI: 10.1103/PhysRevD.10.437
[2] DOI: 10.1090/S0002-9904-1973-13299-9 · Zbl 0274.58003
[3] DOI: 10.1063/1.522814
[4] DOI: 10.1063/1.522814
[5] DOI: 10.1007/BF01645610 · Zbl 0263.53042
[6] DOI: 10.1063/1.527049 · Zbl 0593.53041
[7] DOI: 10.1007/BF00280740 · Zbl 0343.35056
[8] DOI: 10.1007/BF01645486
[9] DOI: 10.1007/BF01209300 · Zbl 0548.53054
[10] DOI: 10.1007/BF02392460 · Zbl 0484.58028
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