Name

dimension

Space-time

Transformation

Kaluza

5

linear approximated/curved

g μ ν g μ ν + k g 3 ν A ν + k g μ 3 A μ + g 44 k

Klein

linear approximated/curved

g μ ν g μ ν + k A μ A ν + k g 3 ν A ν + k g μ 3 A μ + g 44 k

Yun, et al.

4

linear approximated

g μ ν g μ ν + μ A ν + ν A μ + η μ ν Λ

however, t r ( η μ ν ) = 2

curved

g μ ν g μ ν + μ A ν + ν A μ + η μ ν Λ

however, μ A ν + ν A μ = 0 and Λ: constant