Perturbation theory and harmonic gauge propagation in general relativity, a particular example. (English) Zbl 1327.83070
Summary: We study how the changes of coordinates between the class of harmonic coordinates affect the analytical solutions of Einstein’s equations and we apply it to an analytical approach for stationary and axisymmetric solutions of Einstein equation used by J. A. Cabezas et al. [Gen. Relativ. Gravitation 39, No. 6, 707–736 (2007; Zbl 1157.83311)] and J. E. Cuchí et al. [Gen. Relativ. Gravitation 45, No. 7, 1433–1456 (2013; Zbl 1271.83027); erratum ibid. 45, No. 7, 1457 (2013)] to solve the problem of a self-gravitating rigidly rotating perfect fluid compact source.
MSC:
83C15 | Exact solutions to problems in general relativity and gravitational theory |
83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
53Z05 | Applications of differential geometry to physics |
83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
83C55 | Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) |
Keywords:
harmonic coordinates; analytic solutions; Einstein equations; stationary and axisymmetric metrics; perturbation theory; harmonic gauge; general relativityReferences:
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