Metric signature ( $(-, +, +, +)$ )

The metric signature records the signs of the diagonalized nondegenerate metric tensor, equivalently its numbers of negative and positive directions. For a four-dimensional Lorentzian manifold, both

(-, +, +, +)

and its overall negative convention are common. The numerical signs of contractions and component Hodge star operator identities must be consistent with that choice and the orientation.

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In the context of general relativity and differential geometry, a **metric signature** refers to the convention used to describe the character of the components of the metric tensor, which encodes the geometric and causal structure of spacetime. The metric tensor $ g_{\mu\nu} $ is a fundamental object in general relativity that allows for the computation of distances and angles in a given manifold (the mathematical representation of spacetime).

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Ciro Santilli  40 Updated 2025-07-16

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Metric signature ((−,+,+,+))

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