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:
| [1] | Cabezas, JA; Martín, J.; Molina, A.; Ruiz, E., No article title, Gen. Relativ. Gravit., 39, 707-736 (2007) · Zbl 1157.83311 · doi:10.1007/s10714-007-0414-6 |
| [2] | Cuchí, JE; Gil-Rivero, A.; Molina, A.; Ruiz, E., No article title, Gen. Relativ. Gravit., 45, 1433-1456 (2013) · Zbl 1271.83027 · doi:10.1007/s10714-013-1528-7 |
| [3] | Chandrasekhar, S., No article title, ApJ, 142, 1488 (1965) · doi:10.1086/148432 |
| [4] | Chandrasekhar, S.; Nutku, Y., No article title, ApJ, 158, 55 (1969) · doi:10.1086/150171 |
| [5] | Hartle, JB, No article title, ApJ, 150, 1005 (1967) · doi:10.1086/149400 |
| [6] | Thorne, KS, No article title, Rev. Mod. Phys., 52, 299 (1980) · doi:10.1103/RevModPhys.52.299 |
| [7] | Geroch, R., No article title, J. Math. Phys., 11, 1955 (1970) · Zbl 1107.83313 · doi:10.1063/1.1665348 |
| [8] | Hansen, RO, No article title, J. Math. Phys., 15, 46 (1974) · Zbl 1107.83304 · doi:10.1063/1.1666501 |
| [9] | Thorne, K. S. In: Sachs, R. K. (eds.) International School of Physics Enrico Fermi, Course 47 (1969), General Relativity and Cosmology, p. 237. Academic Press, New York, (1971) |
| [10] | Lichnerowicz, A.: Théories relativistes de la Gravitation et de l’Electromagnetisme. Masson, Paris (1955) · Zbl 0065.20704 |
| [11] | Boyer, RH, No article title, Proc. Camb. Philos. Soc., 61, 527 (1965) · Zbl 0127.18202 · doi:10.1017/S0305004100004084 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
