Abstract
We study how the changes of coordinates between the class of harmonic coordinates affect the analitycal solutions of Einstein’s equations and we apply it to an analytical approach for stationary and axisymmetric solutions of Einstein equation used by Cabezas et al. (Gen. Relativ. Gravit. 39:707–736, 2007) and Cuchí et al. (Gen. Relativ. Gravit. 45:1433–1456, 2013) to solve the problem of a self-gravitating rigidly rotating perfect fluid compact source.
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Acknowledgments
This work has been supported by Projects FIS2012-30926 from Ministerio de Economía y Competividad. One of us A.M. also thanks the Universidad de Salamanca for hospitality. The authors thank the anonymous reviewer for its criticism and helpful comments that let us to improve the paper.
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Martín, J., Molina, A. & Ruiz, E. Perturbation theory and harmonic gauge propagation in general relativity, a particular example. Gen Relativ Gravit 47, 112 (2015). https://doi.org/10.1007/s10714-015-1947-8
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DOI: https://doi.org/10.1007/s10714-015-1947-8