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RELATIVITY In Relativity , the Metric Signature could either be +--- or -+++. The latter form is often called the '' Landau - Lifshitz (spacelike) sign convention''. A similar dual convention is used in higher-dimensional relativistic theories. The Ricci Tensor is defined as the contraction of the Riemann Tensor . Some authors use the contraction , whereas others use the alternative . Due to the Symmetries Of The Riemann Tensor , these two definitions differ by a minus sign. In fact the second definition of the Ricci tensor is . The sign of the Ricci tensor does not change, because the two sign conventions concern the sign of the Riemann tensor. The second definition just compensates the sign and it works together with the second definition of the Riemann tensor (see e.g. Barrett O'Neill's Semi-riemannian geometry). THERMODYNAMICS The sign of work in the First Law Of Thermodynamics . OTHER CONVENTIONS
It is often considered good form to state explicitly which sign convention is to be used at the beginning of each book or article. |
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