Manipulating an nxn metric where n is often >4, depending on the model. The 00 component is always tau*constant, as in the Minkowski metric, but the signs on all components might be + or −, depending on the model. Can I call this metric a Minkowski metric?

imire37

imire37

Answered question

2022-08-11

Manipulating an n × n metric where n is often > 4, depending on the model. The 00 component is always τ*constant, as in the Minkowski metric, but the signs on all components might be + or , depending on the model. Can I call this metric a Minkowski metric? Or what should I call it?

Answer & Explanation

Addison Herman

Addison Herman

Beginner2022-08-12Added 15 answers

Just state that pseudo-something metric via reference to its signature ( p , q ).
The metric component (in contrast to the signature) are coordinate system dependend, so this statement is not really true. But even what you intended to say seem strage: in a homogenous space, why would the metric component want to grow with an affine paramert like that?
Landen Miller

Landen Miller

Beginner2022-08-13Added 4 answers

If the coordinates are cover your space, are real, and there no identifications or other topology-changing shenanigans, then this is a pseudo-Euclidean space. That is the proper generalization of Minkowski space with different signatures.
If the coordinates are local, then pseudo-Riemannian. This allows curvature or different topologies, but still requires the signature (num. of positive and negative components) to be the same throughout the space. Additionally, the specific case of signature ( 1 , n ) or ( n , 1 ) is called Lorentzian, though having a Lorentzian metric only implies that the space/manifold is pseudo-Riemannian and not necessarily pseudo-Euclidean.

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