On one connection between Lorentzian and Euclidean metrics

Details On one connection between Lorentzian and Euclidean metrics On one connection between Lorentzian and Euclidean metrics

1998-02-22

arxiv.org/abs/gr-qc/9802057v3

Journal of Geomery and Physics, vol.34 No.3-4, 2000, pp. 321-335

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. Revised: all proofs are significantly

Scientific paper

10.1016/S0393-0440(99)00074-1

We investigate connections between pairs of (pseudo-)Riemannian metrics whose sum is a (tensor) product of a covector field with itself. A bijective mapping between the classes of Euclidean and Lorentzian metrics is constructed as a special result. The existence of such maps on a differentiable manifold is discussed. Similar relations for metrics of arbitrary signature on a manifold are considered. We point the possibility that any physical theory based on real Lorentzian metric(s) can be (re)formulated equivalently in terms of real Euclidean metric(s).

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