Question

Name of vector related to metric tensor?

Answer 1

Suppose we have a locally Minkowskian metric gμνgμν, and we explicitly diagonalize it:

gμν=Uλμ(δλκ−2δ0λδ0κ)Uκνgμν=Uμλ(δλκ−2δ0λδ0κ)Uνκ

where UU is orthogonal. We can then re-distribute UUto find

gμν=δμν−2u^μu^νgμν=δμν−2u^μu^ν

for some unit vector u^

Answer 2

The metric tensor, or just the metric, 2nd rank covariant symmetric, is very commonly used to define the "inner product" or "dot product" of two vectors. ... Faraday's tensor, 2nd rank contravariant antisymmetric, is the tensor that explains electrodynamics and Maxwell's Equations in 4-dimensional relativistic spacetime.