Exponential stretch-rotation (ESR) formulation of general relativity

Details Exponential stretch-rotation (ESR) formulation of general relativity Exponential stretch-rotation (ESR) formulation of general relativity

2003-03-18

arxiv.org/abs/gr-qc/0303065v1

Int.J.Mod.Phys. D13 (2004) 373

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

submitted to Class. Quantum Grav

Scientific paper

10.1142/S021827180400458X

We study a tensorial exponential transformation of a three-dimensional metric of space-like hypersurfaces embedded in a four-dimensional space-time, $\gamma_{ij} = e^{\epsilon_{ikm}\theta_m} e^{\phi_k} e^{-\epsilon_{jkn}\theta_n}$, where $\phi_k$ are logarithms of the eigenvalues of $\gamma_{ij}$, $\theta_k$ 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 $\theta_k$, 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.

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