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).
