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Exponential stretch-rotation (ESR) formulation of general relativity | | A.M. Khokhlov
; I.D. Novikov
; | | Date: |
18 Mar 2003 | | Journal: | Int.J.Mod.Phys. D13 (2004) 373 | | Subject: | gr-qc | | Affiliation: | Naval Research Laboratory, Washington DC, USA) and I.D. Novikov (Theoretical Astrophysics Center, Copenhagen, Denmark | | Abstract: | We study a tensorial exponential transformation of a three-dimensional metric of space-like hypersurfaces embedded in a four-dimensional space-time, $gamma_{ij} = e^{epsilon_{ikm} heta_m} e^{phi_k} e^{-epsilon_{jkn} heta_n}$, where $phi_k$ are logarithms of the eigenvalues of $gamma_{ij}$, $ heta_k$ are rotation angles, and $epsilon_{ijk}$ is a fully anti-symmetric symbol. Evolution part of Einstein’s equations, formulated in terms of $phi_k$ and $ heta_k$, describes time evolution of the metric at every point of a hyper-surface as a continuous stretch and rotation of a local coordinate system in a tangential space. The exponential stretch-rotation (ESR) transformation generalizes particular exponential transformations used previously in cases of spatial symmetry. The ESR 3+1 formulation of Einstein’s equations may have certain advantages for long-term stable integration of these equations. | | Source: | arXiv, gr-qc/0303065 | | Services: | Forum | Review | PDF | Favorites | |
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